Wolfram Researchfunctions.wolfram.comOther Wolfram Sites
Search Site
Function CategoriesGraphics GalleryNotationsGeneral IdentitiesAbout This Site Email Comments

View Related Information In
The Documentation Center
MathWorld

Download All Formulas For This Function
Mathematica Notebook
PDF File

 

Developed with Mathematica -- Download a Free Trial Version
 











MathieuS




Mathematica Notation

Traditional Notation









Mathieu and Spheroidal Functions > MathieuS[a,q,z] > Series representations > Generalized power series > Expansions at q==0





http://functions.wolfram.com/11.02.06.0003.01









  


  








Input Form





MathieuS[MathieuCharacteristicB[r, q], q, z] \[Proportional] Sin[r z] + (1/4) (Sin[(r - 2) z]/(r - 1) - Sin[(r + 2) z]/(r + 1)) q + (1/32) (Sin[(r - 4) z]/((r - 2) (r - 1)) - (2 (r^2 + 1) Sin[r z])/ ((r - 1)^2 (r + 1)^2) + Sin[(r + 4) z]/((r + 1) (r + 2))) q^2 + (1/384) (Sin[(r - 6) z]/((r - 3) (r - 2) (r - 1)) - (3 (r^3 - r^2 - r - 11) Sin[(r - 2) z])/((r - 2) (r - 1)^3 (r + 1)^2) + (3 (r^3 + r^2 - r + 11) Sin[(r + 2) z])/((r - 1)^2 (r + 1)^3 (r + 2)) - Sin[(r + 6) z]/((r + 1) (r + 2) (r + 3))) q^3 + (1/6144) (Sin[(r - 8) z]/((r - 4) (r - 3) (r - 2) (r - 1)) - (4 (r^3 - r^2 - 7 r - 29) Sin[(r - 4) z])/((r - 3) (r - 2) (r - 1)^3 (r + 1)^2) + (6 (r^8 - 15 r^6 - 185 r^4 + 675 r^2 + 316) Sin[r z])/ ((r - 2)^2 (r - 1)^4 (r + 1)^4 (r + 2)^2) - (4 (r^3 + r^2 - 7 r + 29) Sin[(r + 4) z])/((r - 1)^2 (r + 1)^3 (r + 2) (r + 3)) + Sin[(r + 8) z]/((r + 1) (r + 2) (r + 3) (r + 4))) q^4 + (1/122880) (Sin[(r - 10) z]/((r - 5) (r - 4) (r - 3) (r - 2) (r - 1)) - (5 (r^3 - r^2 - 17 r - 55) Sin[(r - 6) z])/((r - 4) (r - 3) (r - 2) (r - 1)^3 (r + 1)^2) + (10 (r^9 - r^8 - 31 r^7 - 5 r^6 - 273 r^5 + 2457 r^4 + 1931 r^3 - 6335 r^2 - 3572 r - 7564) Sin[(r - 2) z])/ ((r - 3) (r - 2)^2 (r - 1)^5 (r + 1)^4 (r + 2)^2) - (10 (r^9 + r^8 - 31 r^7 + 5 r^6 - 273 r^5 - 2457 r^4 + 1931 r^3 + 6335 r^2 - 3572 r + 7564) Sin[(r + 2) z])/((r - 2)^2 (r - 1)^4 (r + 1)^5 (r + 2)^2 (r + 3)) + (5 (r^3 + r^2 - 17 r + 55) Sin[(r + 6) z])/((r - 1)^2 (r + 1)^3 (r + 2) (r + 3) (r + 4)) - Sin[(r + 10) z]/((r + 1) (r + 2) (r + 3) (r + 4) (r + 5))) q^5 + (1/2949120) (Sin[(r - 12) z]/((r - 6) (r - 5) (r - 4) (r - 3) (r - 2) (r - 1)) - (6 (r^3 - r^2 - 31 r - 89) Sin[(r - 8) z])/ ((r - 5) (r - 4) (r - 3) (r - 2) (r - 1)^3 (r + 1)^2) + (15 (r^10 - 3 r^9 - 53 r^8 + 69 r^7 + 145 r^6 + 8211 r^5 - 16879 r^4 - 32025 r^3 + 32954 r^2 + 16404 r + 71528) Sin[(r - 4) z])/ ((r - 4) (r - 3) (r - 2)^3 (r - 1)^5 (r + 1)^4 (r + 2)^2) - (20 (r^14 - 72 r^12 + 597 r^10 + 75244 r^8 - 718317 r^6 + 153312 r^4 + 4883287 r^2 + 1329084) Sin[r z])/((r - 3)^2 (r - 2)^2 (r - 1)^6 (r + 1)^6 (r + 2)^2 (r + 3)^2) + (15 (r^10 + 3 r^9 - 53 r^8 - 69 r^7 + 145 r^6 - 8211 r^5 - 16879 r^4 + 32025 r^3 + 32954 r^2 - 16404 r + 71528) Sin[(r + 4) z])/ ((r - 2)^2 (r - 1)^4 (r + 1)^5 (r + 2)^3 (r + 3) (r + 4)) - (6 (r^3 + r^2 - 31 r + 89) Sin[(r + 8) z])/((r - 1)^2 (r + 1)^3 (r + 2) (r + 3) (r + 4) (r + 5)) + Sin[(r + 12) z]/((r + 1) (r + 2) (r + 3) (r + 4) (r + 5) (r + 6))) q^6 + O[q]^7 /; !(Element[r, Integers] && -6 <= r <= 6)








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["MathieuS", "[", RowBox[List[RowBox[List["MathieuCharacteristicB", "[", RowBox[List["r", ",", "q"]], "]"]], ",", "q", ",", "z"]], "]"]], "\[Proportional]", RowBox[List[RowBox[List["Sin", "[", RowBox[List["r", " ", "z"]], "]"]], "+", RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List[FractionBox[RowBox[List["Sin", "[", RowBox[List[RowBox[List["(", RowBox[List["r", "-", "2"]], ")"]], " ", "z"]], "]"]], RowBox[List["r", "-", "1"]]], "-", FractionBox[RowBox[List["Sin", "[", RowBox[List[RowBox[List["(", RowBox[List["r", "+", "2"]], ")"]], " ", "z"]], "]"]], RowBox[List["r", "+", "1"]]]]], ")"]], "q"]], "+", RowBox[List[FractionBox["1", "32"], " ", RowBox[List["(", RowBox[List[FractionBox[RowBox[List["Sin", "[", RowBox[List[RowBox[List["(", RowBox[List["r", "-", "4"]], ")"]], " ", "z"]], "]"]], RowBox[List[RowBox[List["(", RowBox[List["r", "-", "2"]], ")"]], " ", RowBox[List["(", RowBox[List["r", "-", "1"]], ")"]]]]], "-", FractionBox[RowBox[List["2", " ", RowBox[List["(", RowBox[List[SuperscriptBox["r", "2"], "+", "1"]], ")"]], " ", RowBox[List["Sin", "[", RowBox[List["r", " ", "z"]], "]"]]]], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["r", "-", "1"]], ")"]], "2"], SuperscriptBox[RowBox[List["(", RowBox[List["r", "+", "1"]], ")"]], "2"]]]], "+", FractionBox[RowBox[List["Sin", "[", RowBox[List[RowBox[List["(", RowBox[List["r", "+", "4"]], ")"]], " ", "z"]], "]"]], RowBox[List[RowBox[List["(", RowBox[List["r", "+", "1"]], ")"]], " ", RowBox[List["(", RowBox[List["r", "+", "2"]], ")"]]]]]]], ")"]], SuperscriptBox["q", "2"]]], "+", RowBox[List[FractionBox["1", "384"], " ", RowBox[List["(", RowBox[List[FractionBox[RowBox[List["Sin", "[", RowBox[List[RowBox[List["(", RowBox[List["r", "-", "6"]], ")"]], " ", "z"]], "]"]], RowBox[List[RowBox[List["(", RowBox[List["r", "-", "3"]], ")"]], " ", RowBox[List["(", RowBox[List["r", "-", "2"]], ")"]], " ", RowBox[List["(", RowBox[List["r", "-", "1"]], ")"]]]]], "-", FractionBox[RowBox[List["3", " ", RowBox[List["(", RowBox[List[SuperscriptBox["r", "3"], "-", SuperscriptBox["r", "2"], "-", "r", "-", "11"]], ")"]], " ", RowBox[List["Sin", "[", RowBox[List[RowBox[List["(", RowBox[List["r", "-", "2"]], ")"]], " ", "z"]], "]"]]]], RowBox[List[RowBox[List["(", RowBox[List["r", "-", "2"]], ")"]], SuperscriptBox[RowBox[List["(", RowBox[List["r", "-", "1"]], ")"]], "3"], SuperscriptBox[RowBox[List["(", RowBox[List["r", "+", "1"]], ")"]], "2"]]]], "+", FractionBox[RowBox[List["3", " ", RowBox[List["(", RowBox[List[SuperscriptBox["r", "3"], "+", SuperscriptBox["r", "2"], "-", "r", "+", "11"]], ")"]], " ", RowBox[List["Sin", "[", RowBox[List[RowBox[List["(", RowBox[List["r", "+", "2"]], ")"]], " ", "z"]], "]"]]]], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["r", "-", "1"]], ")"]], "2"], SuperscriptBox[RowBox[List["(", RowBox[List["r", "+", "1"]], ")"]], "3"], RowBox[List["(", RowBox[List["r", "+", "2"]], ")"]]]]], "-", FractionBox[RowBox[List["Sin", "[", RowBox[List[RowBox[List["(", RowBox[List["r", "+", "6"]], ")"]], " ", "z"]], "]"]], RowBox[List[RowBox[List["(", RowBox[List["r", "+", "1"]], ")"]], " ", RowBox[List["(", RowBox[List["r", "+", "2"]], ")"]], " ", RowBox[List["(", RowBox[List["r", "+", "3"]], ")"]]]]]]], ")"]], " ", SuperscriptBox["q", "3"]]], "+", RowBox[List[FractionBox["1", "6144"], " ", RowBox[List["(", RowBox[List[FractionBox[RowBox[List["Sin", "[", RowBox[List[RowBox[List["(", RowBox[List["r", "-", "8"]], ")"]], " ", "z"]], "]"]], RowBox[List[RowBox[List["(", RowBox[List["r", "-", "4"]], ")"]], " ", RowBox[List["(", RowBox[List["r", "-", "3"]], ")"]], " ", RowBox[List["(", RowBox[List["r", "-", "2"]], ")"]], " ", RowBox[List["(", RowBox[List["r", "-", "1"]], ")"]]]]], "-", FractionBox[RowBox[List["4", " ", RowBox[List["(", RowBox[List[SuperscriptBox["r", "3"], "-", SuperscriptBox["r", "2"], "-", RowBox[List["7", " ", "r"]], "-", "29"]], ")"]], " ", RowBox[List["Sin", "[", RowBox[List[RowBox[List["(", RowBox[List["r", "-", "4"]], ")"]], " ", "z"]], "]"]]]], RowBox[List[RowBox[List["(", RowBox[List["r", "-", "3"]], ")"]], " ", RowBox[List["(", RowBox[List["r", "-", "2"]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["r", "-", "1"]], ")"]], "3"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["r", "+", "1"]], ")"]], "2"]]]], "+", FractionBox[RowBox[List["6", " ", RowBox[List["(", RowBox[List[SuperscriptBox["r", "8"], "-", RowBox[List["15", " ", SuperscriptBox["r", "6"]]], "-", RowBox[List["185", " ", SuperscriptBox["r", "4"]]], "+", RowBox[List["675", " ", SuperscriptBox["r", "2"]]], "+", "316"]], ")"]], " ", RowBox[List["Sin", "[", RowBox[List["r", " ", "z"]], "]"]]]], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["r", "-", "2"]], ")"]], "2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["r", "-", "1"]], ")"]], "4"], SuperscriptBox[RowBox[List["(", RowBox[List["r", "+", "1"]], ")"]], "4"], SuperscriptBox[RowBox[List["(", RowBox[List["r", "+", "2"]], ")"]], "2"]]]], "-", FractionBox[RowBox[List["4", " ", RowBox[List["(", RowBox[List[SuperscriptBox["r", "3"], "+", SuperscriptBox["r", "2"], "-", RowBox[List["7", " ", "r"]], "+", "29"]], ")"]], " ", RowBox[List["Sin", "[", RowBox[List[RowBox[List["(", RowBox[List["r", "+", "4"]], ")"]], " ", "z"]], "]"]]]], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["r", "-", "1"]], ")"]], "2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["r", "+", "1"]], ")"]], "3"], " ", RowBox[List["(", RowBox[List["r", "+", "2"]], ")"]], " ", RowBox[List["(", RowBox[List["r", "+", "3"]], ")"]]]]], "+", FractionBox[RowBox[List["Sin", "[", RowBox[List[RowBox[List["(", RowBox[List["r", "+", "8"]], ")"]], " ", "z"]], "]"]], RowBox[List[RowBox[List["(", RowBox[List["r", "+", "1"]], ")"]], " ", RowBox[List["(", RowBox[List["r", "+", "2"]], ")"]], " ", RowBox[List["(", RowBox[List["r", "+", "3"]], ")"]], " ", RowBox[List["(", RowBox[List["r", "+", "4"]], ")"]]]]]]], ")"]], " ", SuperscriptBox["q", "4"]]], "+", RowBox[List[FractionBox["1", "122880"], " ", RowBox[List["(", RowBox[List[FractionBox[RowBox[List["Sin", "[", RowBox[List[RowBox[List["(", RowBox[List["r", "-", "10"]], ")"]], " ", "z"]], "]"]], RowBox[List[RowBox[List["(", RowBox[List["r", "-", "5"]], ")"]], " ", RowBox[List["(", RowBox[List["r", "-", "4"]], ")"]], " ", RowBox[List["(", RowBox[List["r", "-", "3"]], ")"]], " ", RowBox[List["(", RowBox[List["r", "-", "2"]], ")"]], " ", RowBox[List["(", RowBox[List["r", "-", "1"]], ")"]]]]], "-", FractionBox[RowBox[List["5", " ", RowBox[List["(", RowBox[List[SuperscriptBox["r", "3"], "-", SuperscriptBox["r", "2"], "-", RowBox[List["17", " ", "r"]], "-", "55"]], ")"]], " ", RowBox[List["Sin", "[", RowBox[List[RowBox[List["(", RowBox[List["r", "-", "6"]], ")"]], " ", "z"]], "]"]]]], RowBox[List[RowBox[List["(", RowBox[List["r", "-", "4"]], ")"]], " ", RowBox[List["(", RowBox[List["r", "-", "3"]], ")"]], " ", RowBox[List["(", RowBox[List["r", "-", "2"]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["r", "-", "1"]], ")"]], "3"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["r", "+", "1"]], ")"]], "2"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List["10", " ", RowBox[List["(", RowBox[List[SuperscriptBox["r", "9"], "-", SuperscriptBox["r", "8"], "-", RowBox[List["31", " ", SuperscriptBox["r", "7"]]], "-", RowBox[List["5", " ", SuperscriptBox["r", "6"]]], "-", RowBox[List["273", " ", SuperscriptBox["r", "5"]]], "+", RowBox[List["2457", " ", SuperscriptBox["r", "4"]]], "+", RowBox[List["1931", " ", SuperscriptBox["r", "3"]]], "-", RowBox[List["6335", " ", SuperscriptBox["r", "2"]]], "-", RowBox[List["3572", " ", "r"]], "-", "7564"]], ")"]], " ", RowBox[List["Sin", "[", RowBox[List[RowBox[List["(", RowBox[List["r", "-", "2"]], ")"]], " ", "z"]], "]"]]]], ")"]], "/", RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["r", "-", "3"]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["r", "-", "2"]], ")"]], "2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["r", "-", "1"]], ")"]], "5"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["r", "+", "1"]], ")"]], "4"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["r", "+", "2"]], ")"]], "2"]]], ")"]]]], "-", RowBox[List[RowBox[List["(", RowBox[List["10", " ", RowBox[List["(", RowBox[List[SuperscriptBox["r", "9"], "+", SuperscriptBox["r", "8"], "-", RowBox[List["31", " ", SuperscriptBox["r", "7"]]], "+", RowBox[List["5", " ", SuperscriptBox["r", "6"]]], "-", RowBox[List["273", " ", SuperscriptBox["r", "5"]]], "-", RowBox[List["2457", " ", SuperscriptBox["r", "4"]]], "+", RowBox[List["1931", " ", SuperscriptBox["r", "3"]]], "+", RowBox[List["6335", " ", SuperscriptBox["r", "2"]]], "-", RowBox[List["3572", " ", "r"]], "+", "7564"]], ")"]], " ", RowBox[List["Sin", "[", RowBox[List[RowBox[List["(", RowBox[List["r", "+", "2"]], ")"]], " ", "z"]], "]"]]]], ")"]], "/", RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["r", "-", "2"]], ")"]], "2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["r", "-", "1"]], ")"]], "4"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["r", "+", "1"]], ")"]], "5"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["r", "+", "2"]], ")"]], "2"], RowBox[List["(", RowBox[List["r", "+", "3"]], ")"]]]], ")"]]]], "+", FractionBox[RowBox[List["5", " ", RowBox[List["(", RowBox[List[SuperscriptBox["r", "3"], "+", SuperscriptBox["r", "2"], "-", RowBox[List["17", " ", "r"]], "+", "55"]], ")"]], " ", RowBox[List["Sin", "[", RowBox[List[RowBox[List["(", RowBox[List["r", "+", "6"]], ")"]], " ", "z"]], "]"]]]], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["r", "-", "1"]], ")"]], "2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["r", "+", "1"]], ")"]], "3"], " ", RowBox[List["(", RowBox[List["r", "+", "2"]], ")"]], " ", RowBox[List["(", RowBox[List["r", "+", "3"]], ")"]], " ", RowBox[List["(", RowBox[List["r", "+", "4"]], ")"]]]]], "-", FractionBox[RowBox[List["Sin", "[", RowBox[List[RowBox[List["(", RowBox[List["r", "+", "10"]], ")"]], " ", "z"]], "]"]], RowBox[List[RowBox[List["(", RowBox[List["r", "+", "1"]], ")"]], " ", RowBox[List["(", RowBox[List["r", "+", "2"]], ")"]], " ", RowBox[List["(", RowBox[List["r", "+", "3"]], ")"]], " ", RowBox[List["(", RowBox[List["r", "+", "4"]], ")"]], " ", RowBox[List["(", RowBox[List["r", "+", "5"]], ")"]]]]]]], ")"]], " ", SuperscriptBox["q", "5"]]], "+", RowBox[List[FractionBox["1", "2949120"], " ", RowBox[List["(", RowBox[List[FractionBox[RowBox[List["Sin", "[", RowBox[List[RowBox[List["(", RowBox[List["r", "-", "12"]], ")"]], " ", "z"]], "]"]], RowBox[List[RowBox[List["(", RowBox[List["r", "-", "6"]], ")"]], " ", RowBox[List["(", RowBox[List["r", "-", "5"]], ")"]], " ", RowBox[List["(", RowBox[List["r", "-", "4"]], ")"]], " ", RowBox[List["(", RowBox[List["r", "-", "3"]], ")"]], " ", RowBox[List["(", RowBox[List["r", "-", "2"]], ")"]], " ", RowBox[List["(", RowBox[List["r", "-", "1"]], ")"]]]]], "-", FractionBox[RowBox[List["6", " ", RowBox[List["(", RowBox[List[SuperscriptBox["r", "3"], "-", SuperscriptBox["r", "2"], "-", RowBox[List["31", " ", "r"]], "-", "89"]], ")"]], " ", RowBox[List["Sin", "[", RowBox[List[RowBox[List["(", RowBox[List["r", "-", "8"]], ")"]], " ", "z"]], "]"]]]], RowBox[List[RowBox[List["(", RowBox[List["r", "-", "5"]], ")"]], " ", RowBox[List["(", RowBox[List["r", "-", "4"]], ")"]], " ", RowBox[List["(", RowBox[List["r", "-", "3"]], ")"]], " ", RowBox[List["(", RowBox[List["r", "-", "2"]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["r", "-", "1"]], ")"]], "3"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["r", "+", "1"]], ")"]], "2"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List["15", " ", RowBox[List["(", RowBox[List[SuperscriptBox["r", "10"], "-", RowBox[List["3", " ", SuperscriptBox["r", "9"]]], "-", RowBox[List["53", " ", SuperscriptBox["r", "8"]]], "+", RowBox[List["69", " ", SuperscriptBox["r", "7"]]], "+", RowBox[List["145", " ", SuperscriptBox["r", "6"]]], "+", RowBox[List["8211", " ", SuperscriptBox["r", "5"]]], "-", RowBox[List["16879", " ", SuperscriptBox["r", "4"]]], "-", RowBox[List["32025", " ", SuperscriptBox["r", "3"]]], "+", RowBox[List["32954", " ", SuperscriptBox["r", "2"]]], "+", RowBox[List["16404", " ", "r"]], "+", "71528"]], ")"]], " ", RowBox[List["Sin", "[", RowBox[List[RowBox[List["(", RowBox[List["r", "-", "4"]], ")"]], " ", "z"]], "]"]]]], ")"]], "/", RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["r", "-", "4"]], ")"]], " ", RowBox[List["(", RowBox[List["r", "-", "3"]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["r", "-", "2"]], ")"]], "3"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["r", "-", "1"]], ")"]], "5"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["r", "+", "1"]], ")"]], "4"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["r", "+", "2"]], ")"]], "2"]]], ")"]]]], "-", RowBox[List[RowBox[List["(", RowBox[List["20", " ", RowBox[List["(", RowBox[List[SuperscriptBox["r", "14"], "-", RowBox[List["72", " ", SuperscriptBox["r", "12"]]], "+", RowBox[List["597", " ", SuperscriptBox["r", "10"]]], "+", RowBox[List["75244", " ", SuperscriptBox["r", "8"]]], "-", RowBox[List["718317", " ", SuperscriptBox["r", "6"]]], "+", RowBox[List["153312", " ", SuperscriptBox["r", "4"]]], "+", RowBox[List["4883287", " ", SuperscriptBox["r", "2"]]], "+", "1329084"]], ")"]], " ", RowBox[List["Sin", "[", RowBox[List["r", " ", "z"]], "]"]]]], ")"]], "/", RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["r", "-", "3"]], ")"]], "2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["r", "-", "2"]], ")"]], "2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["r", "-", "1"]], ")"]], "6"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["r", "+", "1"]], ")"]], "6"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["r", "+", "2"]], ")"]], "2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["r", "+", "3"]], ")"]], "2"]]], ")"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List["15", " ", RowBox[List["(", RowBox[List[SuperscriptBox["r", "10"], "+", RowBox[List["3", " ", SuperscriptBox["r", "9"]]], "-", RowBox[List["53", " ", SuperscriptBox["r", "8"]]], "-", RowBox[List["69", " ", SuperscriptBox["r", "7"]]], "+", RowBox[List["145", " ", SuperscriptBox["r", "6"]]], "-", RowBox[List["8211", " ", SuperscriptBox["r", "5"]]], "-", RowBox[List["16879", " ", SuperscriptBox["r", "4"]]], "+", RowBox[List["32025", " ", SuperscriptBox["r", "3"]]], "+", RowBox[List["32954", " ", SuperscriptBox["r", "2"]]], "-", RowBox[List["16404", " ", "r"]], "+", "71528"]], ")"]], " ", RowBox[List["Sin", "[", RowBox[List[RowBox[List["(", RowBox[List["r", "+", "4"]], ")"]], " ", "z"]], "]"]]]], ")"]], "/", RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["r", "-", "2"]], ")"]], "2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["r", "-", "1"]], ")"]], "4"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["r", "+", "1"]], ")"]], "5"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["r", "+", "2"]], ")"]], "3"], " ", RowBox[List["(", RowBox[List["r", "+", "3"]], ")"]], " ", RowBox[List["(", RowBox[List["r", "+", "4"]], ")"]]]], ")"]]]], "-", FractionBox[RowBox[List["6", " ", RowBox[List["(", RowBox[List[SuperscriptBox["r", "3"], "+", SuperscriptBox["r", "2"], "-", RowBox[List["31", " ", "r"]], "+", "89"]], ")"]], " ", RowBox[List["Sin", "[", RowBox[List[RowBox[List["(", RowBox[List["r", "+", "8"]], ")"]], " ", "z"]], "]"]]]], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["r", "-", "1"]], ")"]], "2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["r", "+", "1"]], ")"]], "3"], " ", RowBox[List["(", RowBox[List["r", "+", "2"]], ")"]], " ", RowBox[List["(", RowBox[List["r", "+", "3"]], ")"]], " ", RowBox[List["(", RowBox[List["r", "+", "4"]], ")"]], " ", RowBox[List["(", RowBox[List["r", "+", "5"]], ")"]]]]], "+", FractionBox[RowBox[List["Sin", "[", RowBox[List[RowBox[List["(", RowBox[List["r", "+", "12"]], ")"]], " ", "z"]], "]"]], RowBox[List[RowBox[List["(", RowBox[List["r", "+", "1"]], ")"]], " ", RowBox[List["(", RowBox[List["r", "+", "2"]], ")"]], " ", RowBox[List["(", RowBox[List["r", "+", "3"]], ")"]], " ", RowBox[List["(", RowBox[List["r", "+", "4"]], ")"]], " ", RowBox[List["(", RowBox[List["r", "+", "5"]], ")"]], " ", RowBox[List["(", RowBox[List["r", "+", "6"]], ")"]]]]]]], ")"]], " ", SuperscriptBox["q", "6"]]], "+", SuperscriptBox[RowBox[List["O", "[", "q", "]"]], "7"]]]]], "/;", RowBox[List["Not", "[", RowBox[List[RowBox[List["r", "\[Element]", "Integers"]], "\[And]", RowBox[List[RowBox[List["-", "6"]], "\[LessEqual]", "r", "\[LessEqual]", "6"]]]], "]"]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <mi> Se </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <msub> <mi> b </mi> <mi> r </mi> </msub> <mo> ( </mo> <mi> q </mi> <mo> ) </mo> </mrow> <mo> , </mo> <mi> q </mi> <mo> , </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8733; </mo> <mrow> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> r </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 4 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mfrac> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mi> r </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </mfrac> <mo> - </mo> <mfrac> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mi> r </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </mfrac> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> q </mi> </mrow> <mo> + </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 32 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mfrac> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> - </mo> <mn> 4 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mi> r </mi> <mn> 2 </mn> </msup> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> r </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> </mfrac> <mo> + </mo> <mfrac> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 4 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 384 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mfrac> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> - </mo> <mn> 6 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> - </mo> <mn> 3 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 3 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mi> r </mi> <mn> 3 </mn> </msup> <mo> - </mo> <msup> <mi> r </mi> <mn> 2 </mn> </msup> <mo> - </mo> <mi> r </mi> <mo> - </mo> <mn> 11 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 3 </mn> </msup> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 3 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mi> r </mi> <mn> 3 </mn> </msup> <mo> + </mo> <msup> <mi> r </mi> <mn> 2 </mn> </msup> <mo> - </mo> <mi> r </mi> <mo> + </mo> <mn> 11 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 3 </mn> </msup> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> <mo> - </mo> <mfrac> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 6 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 3 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 6144 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mfrac> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> - </mo> <mn> 8 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> - </mo> <mn> 4 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> - </mo> <mn> 3 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mi> r </mi> <mn> 3 </mn> </msup> <mo> - </mo> <msup> <mi> r </mi> <mn> 2 </mn> </msup> <mo> - </mo> <mrow> <mn> 7 </mn> <mo> &#8290; </mo> <mi> r </mi> </mrow> <mo> - </mo> <mn> 29 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> - </mo> <mn> 4 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> - </mo> <mn> 3 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 3 </mn> </msup> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 6 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mi> r </mi> <mn> 8 </mn> </msup> <mo> - </mo> <mrow> <mn> 15 </mn> <mo> &#8290; </mo> <msup> <mi> r </mi> <mn> 6 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 185 </mn> <mo> &#8290; </mo> <msup> <mi> r </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 675 </mn> <mo> &#8290; </mo> <msup> <mi> r </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mn> 316 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> r </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 4 </mn> </msup> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 4 </mn> </msup> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mi> r </mi> <mn> 3 </mn> </msup> <mo> + </mo> <msup> <mi> r </mi> <mn> 2 </mn> </msup> <mo> - </mo> <mrow> <mn> 7 </mn> <mo> &#8290; </mo> <mi> r </mi> </mrow> <mo> + </mo> <mn> 29 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 4 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 3 </mn> </msup> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 3 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> <mo> + </mo> <mfrac> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 8 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 3 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 4 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 122880 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mfrac> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> - </mo> <mn> 10 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> - </mo> <mn> 5 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> - </mo> <mn> 4 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> - </mo> <mn> 3 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 5 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mi> r </mi> <mn> 3 </mn> </msup> <mo> - </mo> <msup> <mi> r </mi> <mn> 2 </mn> </msup> <mo> - </mo> <mrow> <mn> 17 </mn> <mo> &#8290; </mo> <mi> r </mi> </mrow> <mo> - </mo> <mn> 55 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> - </mo> <mn> 6 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> - </mo> <mn> 4 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> - </mo> <mn> 3 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 3 </mn> </msup> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> </mfrac> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mn> 10 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mi> r </mi> <mn> 9 </mn> </msup> <mo> - </mo> <msup> <mi> r </mi> <mn> 8 </mn> </msup> <mo> - </mo> <mrow> <mn> 31 </mn> <mo> &#8290; </mo> <msup> <mi> r </mi> <mn> 7 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 5 </mn> <mo> &#8290; </mo> <msup> <mi> r </mi> <mn> 6 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 273 </mn> <mo> &#8290; </mo> <msup> <mi> r </mi> <mn> 5 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2457 </mn> <mo> &#8290; </mo> <msup> <mi> r </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 1931 </mn> <mo> &#8290; </mo> <msup> <mi> r </mi> <mn> 3 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 6335 </mn> <mo> &#8290; </mo> <msup> <mi> r </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 3572 </mn> <mo> &#8290; </mo> <mi> r </mi> </mrow> <mo> - </mo> <mn> 7564 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> / </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> - </mo> <mn> 3 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 5 </mn> </msup> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 4 </mn> </msup> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mn> 10 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mi> r </mi> <mn> 9 </mn> </msup> <mo> + </mo> <msup> <mi> r </mi> <mn> 8 </mn> </msup> <mo> - </mo> <mrow> <mn> 31 </mn> <mo> &#8290; </mo> <msup> <mi> r </mi> <mn> 7 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 5 </mn> <mo> &#8290; </mo> <msup> <mi> r </mi> <mn> 6 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 273 </mn> <mo> &#8290; </mo> <msup> <mi> r </mi> <mn> 5 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 2457 </mn> <mo> &#8290; </mo> <msup> <mi> r </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 1931 </mn> <mo> &#8290; </mo> <msup> <mi> r </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 6335 </mn> <mo> &#8290; </mo> <msup> <mi> r </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 3572 </mn> <mo> &#8290; </mo> <mi> r </mi> </mrow> <mo> + </mo> <mn> 7564 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> / </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 4 </mn> </msup> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 5 </mn> </msup> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 3 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mfrac> <mrow> <mn> 5 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mi> r </mi> <mn> 3 </mn> </msup> <mo> + </mo> <msup> <mi> r </mi> <mn> 2 </mn> </msup> <mo> - </mo> <mrow> <mn> 17 </mn> <mo> &#8290; </mo> <mi> r </mi> </mrow> <mo> + </mo> <mn> 55 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 6 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 3 </mn> </msup> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 3 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 4 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> <mo> - </mo> <mfrac> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 10 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 3 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 4 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 5 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 5 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 2949120 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mfrac> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> - </mo> <mn> 12 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> - </mo> <mn> 6 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> - </mo> <mn> 5 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> - </mo> <mn> 4 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> - </mo> <mn> 3 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 6 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mi> r </mi> <mn> 3 </mn> </msup> <mo> - </mo> <msup> <mi> r </mi> <mn> 2 </mn> </msup> <mo> - </mo> <mrow> <mn> 31 </mn> <mo> &#8290; </mo> <mi> r </mi> </mrow> <mo> - </mo> <mn> 89 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> - </mo> <mn> 8 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> - </mo> <mn> 5 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> - </mo> <mn> 4 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> - </mo> <mn> 3 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 3 </mn> </msup> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> </mfrac> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mn> 15 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mi> r </mi> <mn> 10 </mn> </msup> <mo> - </mo> <mrow> <mn> 3 </mn> <mo> &#8290; </mo> <msup> <mi> r </mi> <mn> 9 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 53 </mn> <mo> &#8290; </mo> <msup> <mi> r </mi> <mn> 8 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 69 </mn> <mo> &#8290; </mo> <msup> <mi> r </mi> <mn> 7 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 145 </mn> <mo> &#8290; </mo> <msup> <mi> r </mi> <mn> 6 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 8211 </mn> <mo> &#8290; </mo> <msup> <mi> r </mi> <mn> 5 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 16879 </mn> <mo> &#8290; </mo> <msup> <mi> r </mi> <mn> 4 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 32025 </mn> <mo> &#8290; </mo> <msup> <mi> r </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 32954 </mn> <mo> &#8290; </mo> <msup> <mi> r </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 16404 </mn> <mo> &#8290; </mo> <mi> r </mi> </mrow> <mo> + </mo> <mn> 71528 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> - </mo> <mn> 4 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> / </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> - </mo> <mn> 4 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> - </mo> <mn> 3 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 3 </mn> </msup> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 5 </mn> </msup> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 4 </mn> </msup> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mn> 20 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mi> r </mi> <mn> 14 </mn> </msup> <mo> - </mo> <mrow> <mn> 72 </mn> <mo> &#8290; </mo> <msup> <mi> r </mi> <mn> 12 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 597 </mn> <mo> &#8290; </mo> <msup> <mi> r </mi> <mn> 10 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 75244 </mn> <mo> &#8290; </mo> <msup> <mi> r </mi> <mn> 8 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 718317 </mn> <mo> &#8290; </mo> <msup> <mi> r </mi> <mn> 6 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 153312 </mn> <mo> &#8290; </mo> <msup> <mi> r </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 4883287 </mn> <mo> &#8290; </mo> <msup> <mi> r </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mn> 1329084 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> r </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> / </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> - </mo> <mn> 3 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 6 </mn> </msup> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 6 </mn> </msup> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 3 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mn> 15 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mi> r </mi> <mn> 10 </mn> </msup> <mo> + </mo> <mrow> <mn> 3 </mn> <mo> &#8290; </mo> <msup> <mi> r </mi> <mn> 9 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 53 </mn> <mo> &#8290; </mo> <msup> <mi> r </mi> <mn> 8 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 69 </mn> <mo> &#8290; </mo> <msup> <mi> r </mi> <mn> 7 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 145 </mn> <mo> &#8290; </mo> <msup> <mi> r </mi> <mn> 6 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 8211 </mn> <mo> &#8290; </mo> <msup> <mi> r </mi> <mn> 5 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 16879 </mn> <mo> &#8290; </mo> <msup> <mi> r </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 32025 </mn> <mo> &#8290; </mo> <msup> <mi> r </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 32954 </mn> <mo> &#8290; </mo> <msup> <mi> r </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 16404 </mn> <mo> &#8290; </mo> <mi> r </mi> </mrow> <mo> + </mo> <mn> 71528 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 4 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> / </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 4 </mn> </msup> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 5 </mn> </msup> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 3 </mn> </msup> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 3 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 4 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mfrac> <mrow> <mn> 6 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mi> r </mi> <mn> 3 </mn> </msup> <mo> + </mo> <msup> <mi> r </mi> <mn> 2 </mn> </msup> <mo> - </mo> <mrow> <mn> 31 </mn> <mo> &#8290; </mo> <mi> r </mi> </mrow> <mo> + </mo> <mn> 89 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 8 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 3 </mn> </msup> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 3 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 4 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 5 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> <mo> + </mo> <mfrac> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 12 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 3 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 4 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 5 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 6 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 6 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mi> O </mi> <mo> &#8289; </mo> <mo> ( </mo> <msup> <mi> q </mi> <mn> 7 </mn> </msup> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mo> &#172; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> r </mi> <mo> &#8712; </mo> <semantics> <mi> &#8484; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalZ]&quot;, Function[Integers]] </annotation> </semantics> </mrow> <mo> &#8743; </mo> <mrow> <mrow> <mo> - </mo> <mn> 6 </mn> </mrow> <mo> &#8804; </mo> <mi> r </mi> <mo> &#8804; </mo> <mn> 6 </mn> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <ci> Proportional </ci> <apply> <ci> Se </ci> <apply> <apply> <ci> Subscript </ci> <ci> b </ci> <ci> r </ci> </apply> <ci> q </ci> </apply> <ci> q </ci> <ci> z </ci> </apply> <apply> <plus /> <apply> <sin /> <apply> <times /> <ci> r </ci> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 4 </cn> <apply> <plus /> <apply> <times /> <apply> <sin /> <apply> <times /> <apply> <plus /> <ci> r </ci> <cn type='integer'> -2 </cn> </apply> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <plus /> <ci> r </ci> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <sin /> <apply> <times /> <apply> <plus /> <ci> r </ci> <cn type='integer'> 2 </cn> </apply> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <plus /> <ci> r </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <ci> q </ci> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 32 </cn> <apply> <plus /> <apply> <times /> <apply> <sin /> <apply> <times /> <apply> <plus /> <ci> r </ci> <cn type='integer'> -4 </cn> </apply> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <plus /> <ci> r </ci> <cn type='integer'> -2 </cn> </apply> <apply> <plus /> <ci> r </ci> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <apply> <power /> <ci> r </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <sin /> <apply> <times /> <ci> r </ci> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <power /> <apply> <plus /> <ci> r </ci> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <ci> r </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <apply> <sin /> <apply> <times /> <apply> <plus /> <ci> r </ci> <cn type='integer'> 4 </cn> </apply> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <plus /> <ci> r </ci> <cn type='integer'> 1 </cn> </apply> <apply> <plus /> <ci> r </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <ci> q </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 384 </cn> <apply> <plus /> <apply> <times /> <apply> <sin /> <apply> <times /> <apply> <plus /> <ci> r </ci> <cn type='integer'> -6 </cn> </apply> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <plus /> <ci> r </ci> <cn type='integer'> -3 </cn> </apply> <apply> <plus /> <ci> r </ci> <cn type='integer'> -2 </cn> </apply> <apply> <plus /> <ci> r </ci> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 3 </cn> <apply> <plus /> <apply> <power /> <ci> r </ci> <cn type='integer'> 3 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> r </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> r </ci> </apply> <cn type='integer'> -11 </cn> </apply> <apply> <sin /> <apply> <times /> <apply> <plus /> <ci> r </ci> <cn type='integer'> -2 </cn> </apply> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <plus /> <ci> r </ci> <cn type='integer'> -2 </cn> </apply> <apply> <power /> <apply> <plus /> <ci> r </ci> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> 3 </cn> </apply> <apply> <power /> <apply> <plus /> <ci> r </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 3 </cn> <apply> <plus /> <apply> <power /> <ci> r </ci> <cn type='integer'> 3 </cn> </apply> <apply> <power /> <ci> r </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> r </ci> </apply> <cn type='integer'> 11 </cn> </apply> <apply> <sin /> <apply> <times /> <apply> <plus /> <ci> r </ci> <cn type='integer'> 2 </cn> </apply> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <power /> <apply> <plus /> <ci> r </ci> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <ci> r </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 3 </cn> </apply> <apply> <plus /> <ci> r </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <sin /> <apply> <times /> <apply> <plus /> <ci> r </ci> <cn type='integer'> 6 </cn> </apply> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <plus /> <ci> r </ci> <cn type='integer'> 1 </cn> </apply> <apply> <plus /> <ci> r </ci> <cn type='integer'> 2 </cn> </apply> <apply> <plus /> <ci> r </ci> <cn type='integer'> 3 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <power /> <ci> q </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 6144 </cn> <apply> <plus /> <apply> <times /> <apply> <sin /> <apply> <times /> <apply> <plus /> <ci> r </ci> <cn type='integer'> -8 </cn> </apply> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <plus /> <ci> r </ci> <cn type='integer'> -4 </cn> </apply> <apply> <plus /> <ci> r </ci> <cn type='integer'> -3 </cn> </apply> <apply> <plus /> <ci> r </ci> <cn type='integer'> -2 </cn> </apply> <apply> <plus /> <ci> r </ci> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <plus /> <apply> <power /> <ci> r </ci> <cn type='integer'> 3 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> r </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 7 </cn> <ci> r </ci> </apply> </apply> <cn type='integer'> -29 </cn> </apply> <apply> <sin /> <apply> <times /> <apply> <plus /> <ci> r </ci> <cn type='integer'> -4 </cn> </apply> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <plus /> <ci> r </ci> <cn type='integer'> -3 </cn> </apply> <apply> <plus /> <ci> r </ci> <cn type='integer'> -2 </cn> </apply> <apply> <power /> <apply> <plus /> <ci> r </ci> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> 3 </cn> </apply> <apply> <power /> <apply> <plus /> <ci> r </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 6 </cn> <apply> <plus /> <apply> <power /> <ci> r </ci> <cn type='integer'> 8 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 15 </cn> <apply> <power /> <ci> r </ci> <cn type='integer'> 6 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 185 </cn> <apply> <power /> <ci> r </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 675 </cn> <apply> <power /> <ci> r </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> 316 </cn> </apply> <apply> <sin /> <apply> <times /> <ci> r </ci> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <power /> <apply> <plus /> <ci> r </ci> <cn type='integer'> -2 </cn> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <ci> r </ci> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> 4 </cn> </apply> <apply> <power /> <apply> <plus /> <ci> r </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 4 </cn> </apply> <apply> <power /> <apply> <plus /> <ci> r </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <plus /> <apply> <power /> <ci> r </ci> <cn type='integer'> 3 </cn> </apply> <apply> <power /> <ci> r </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 7 </cn> <ci> r </ci> </apply> </apply> <cn type='integer'> 29 </cn> </apply> <apply> <sin /> <apply> <times /> <apply> <plus /> <ci> r </ci> <cn type='integer'> 4 </cn> </apply> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <power /> <apply> <plus /> <ci> r </ci> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <ci> r </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 3 </cn> </apply> <apply> <plus /> <ci> r </ci> <cn type='integer'> 2 </cn> </apply> <apply> <plus /> <ci> r </ci> <cn type='integer'> 3 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <apply> <sin /> <apply> <times /> <apply> <plus /> <ci> r </ci> <cn type='integer'> 8 </cn> </apply> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <plus /> <ci> r </ci> <cn type='integer'> 1 </cn> </apply> <apply> <plus /> <ci> r </ci> <cn type='integer'> 2 </cn> </apply> <apply> <plus /> <ci> r </ci> <cn type='integer'> 3 </cn> </apply> <apply> <plus /> <ci> r </ci> <cn type='integer'> 4 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <ci> q </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 122880 </cn> <apply> <plus /> <apply> <times /> <apply> <sin /> <apply> <times /> <apply> <plus /> <ci> r </ci> <cn type='integer'> -10 </cn> </apply> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <plus /> <ci> r </ci> <cn type='integer'> -5 </cn> </apply> <apply> <plus /> <ci> r </ci> <cn type='integer'> -4 </cn> </apply> <apply> <plus /> <ci> r </ci> <cn type='integer'> -3 </cn> </apply> <apply> <plus /> <ci> r </ci> <cn type='integer'> -2 </cn> </apply> <apply> <plus /> <ci> r </ci> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 5 </cn> <apply> <plus /> <apply> <power /> <ci> r </ci> <cn type='integer'> 3 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> r </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 17 </cn> <ci> r </ci> </apply> </apply> <cn type='integer'> -55 </cn> </apply> <apply> <sin /> <apply> <times /> <apply> <plus /> <ci> r </ci> <cn type='integer'> -6 </cn> </apply> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <plus /> <ci> r </ci> <cn type='integer'> -4 </cn> </apply> <apply> <plus /> <ci> r </ci> <cn type='integer'> -3 </cn> </apply> <apply> <plus /> <ci> r </ci> <cn type='integer'> -2 </cn> </apply> <apply> <power /> <apply> <plus /> <ci> r </ci> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> 3 </cn> </apply> <apply> <power /> <apply> <plus /> <ci> r </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 10 </cn> <apply> <plus /> <apply> <power /> <ci> r </ci> <cn type='integer'> 9 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> r </ci> <cn type='integer'> 8 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 31 </cn> <apply> <power /> <ci> r </ci> <cn type='integer'> 7 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 5 </cn> <apply> <power /> <ci> r </ci> <cn type='integer'> 6 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 273 </cn> <apply> <power /> <ci> r </ci> <cn type='integer'> 5 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 2457 </cn> <apply> <power /> <ci> r </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 1931 </cn> <apply> <power /> <ci> r </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 6335 </cn> <apply> <power /> <ci> r </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 3572 </cn> <ci> r </ci> </apply> </apply> <cn type='integer'> -7564 </cn> </apply> <apply> <sin /> <apply> <times /> <apply> <plus /> <ci> r </ci> <cn type='integer'> -2 </cn> </apply> <ci> z </ci> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <plus /> <ci> r </ci> <cn type='integer'> -3 </cn> </apply> <apply> <power /> <apply> <plus /> <ci> r </ci> <cn type='integer'> -2 </cn> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <ci> r </ci> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> 5 </cn> </apply> <apply> <power /> <apply> <plus /> <ci> r </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 4 </cn> </apply> <apply> <power /> <apply> <plus /> <ci> r </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <times /> <cn type='integer'> 10 </cn> <apply> <plus /> <apply> <power /> <ci> r </ci> <cn type='integer'> 9 </cn> </apply> <apply> <power /> <ci> r </ci> <cn type='integer'> 8 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 31 </cn> <apply> <power /> <ci> r </ci> <cn type='integer'> 7 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 5 </cn> <apply> <power /> <ci> r </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 273 </cn> <apply> <power /> <ci> r </ci> <cn type='integer'> 5 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2457 </cn> <apply> <power /> <ci> r </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 1931 </cn> <apply> <power /> <ci> r </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 6335 </cn> <apply> <power /> <ci> r </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 3572 </cn> <ci> r </ci> </apply> </apply> <cn type='integer'> 7564 </cn> </apply> <apply> <sin /> <apply> <times /> <apply> <plus /> <ci> r </ci> <cn type='integer'> 2 </cn> </apply> <ci> z </ci> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <power /> <apply> <plus /> <ci> r </ci> <cn type='integer'> -2 </cn> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <ci> r </ci> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> 4 </cn> </apply> <apply> <power /> <apply> <plus /> <ci> r </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 5 </cn> </apply> <apply> <power /> <apply> <plus /> <ci> r </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <plus /> <ci> r </ci> <cn type='integer'> 3 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 5 </cn> <apply> <plus /> <apply> <power /> <ci> r </ci> <cn type='integer'> 3 </cn> </apply> <apply> <power /> <ci> r </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 17 </cn> <ci> r </ci> </apply> </apply> <cn type='integer'> 55 </cn> </apply> <apply> <sin /> <apply> <times /> <apply> <plus /> <ci> r </ci> <cn type='integer'> 6 </cn> </apply> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <power /> <apply> <plus /> <ci> r </ci> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <ci> r </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 3 </cn> </apply> <apply> <plus /> <ci> r </ci> <cn type='integer'> 2 </cn> </apply> <apply> <plus /> <ci> r </ci> <cn type='integer'> 3 </cn> </apply> <apply> <plus /> <ci> r </ci> <cn type='integer'> 4 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <sin /> <apply> <times /> <apply> <plus /> <ci> r </ci> <cn type='integer'> 10 </cn> </apply> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <plus /> <ci> r </ci> <cn type='integer'> 1 </cn> </apply> <apply> <plus /> <ci> r </ci> <cn type='integer'> 2 </cn> </apply> <apply> <plus /> <ci> r </ci> <cn type='integer'> 3 </cn> </apply> <apply> <plus /> <ci> r </ci> <cn type='integer'> 4 </cn> </apply> <apply> <plus /> <ci> r </ci> <cn type='integer'> 5 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <power /> <ci> q </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 2949120 </cn> <apply> <plus /> <apply> <times /> <apply> <sin /> <apply> <times /> <apply> <plus /> <ci> r </ci> <cn type='integer'> -12 </cn> </apply> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <plus /> <ci> r </ci> <cn type='integer'> -6 </cn> </apply> <apply> <plus /> <ci> r </ci> <cn type='integer'> -5 </cn> </apply> <apply> <plus /> <ci> r </ci> <cn type='integer'> -4 </cn> </apply> <apply> <plus /> <ci> r </ci> <cn type='integer'> -3 </cn> </apply> <apply> <plus /> <ci> r </ci> <cn type='integer'> -2 </cn> </apply> <apply> <plus /> <ci> r </ci> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 6 </cn> <apply> <plus /> <apply> <power /> <ci> r </ci> <cn type='integer'> 3 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> r </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 31 </cn> <ci> r </ci> </apply> </apply> <cn type='integer'> -89 </cn> </apply> <apply> <sin /> <apply> <times /> <apply> <plus /> <ci> r </ci> <cn type='integer'> -8 </cn> </apply> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <plus /> <ci> r </ci> <cn type='integer'> -5 </cn> </apply> <apply> <plus /> <ci> r </ci> <cn type='integer'> -4 </cn> </apply> <apply> <plus /> <ci> r </ci> <cn type='integer'> -3 </cn> </apply> <apply> <plus /> <ci> r </ci> <cn type='integer'> -2 </cn> </apply> <apply> <power /> <apply> <plus /> <ci> r </ci> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> 3 </cn> </apply> <apply> <power /> <apply> <plus /> <ci> r </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 15 </cn> <apply> <plus /> <apply> <power /> <ci> r </ci> <cn type='integer'> 10 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 3 </cn> <apply> <power /> <ci> r </ci> <cn type='integer'> 9 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 53 </cn> <apply> <power /> <ci> r </ci> <cn type='integer'> 8 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 69 </cn> <apply> <power /> <ci> r </ci> <cn type='integer'> 7 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 145 </cn> <apply> <power /> <ci> r </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 8211 </cn> <apply> <power /> <ci> r </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 16879 </cn> <apply> <power /> <ci> r </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 32025 </cn> <apply> <power /> <ci> r </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 32954 </cn> <apply> <power /> <ci> r </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 16404 </cn> <ci> r </ci> </apply> <cn type='integer'> 71528 </cn> </apply> <apply> <sin /> <apply> <times /> <apply> <plus /> <ci> r </ci> <cn type='integer'> -4 </cn> </apply> <ci> z </ci> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <plus /> <ci> r </ci> <cn type='integer'> -4 </cn> </apply> <apply> <plus /> <ci> r </ci> <cn type='integer'> -3 </cn> </apply> <apply> <power /> <apply> <plus /> <ci> r </ci> <cn type='integer'> -2 </cn> </apply> <cn type='integer'> 3 </cn> </apply> <apply> <power /> <apply> <plus /> <ci> r </ci> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> 5 </cn> </apply> <apply> <power /> <apply> <plus /> <ci> r </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 4 </cn> </apply> <apply> <power /> <apply> <plus /> <ci> r </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <times /> <cn type='integer'> 20 </cn> <apply> <plus /> <apply> <power /> <ci> r </ci> <cn type='integer'> 14 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 72 </cn> <apply> <power /> <ci> r </ci> <cn type='integer'> 12 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 597 </cn> <apply> <power /> <ci> r </ci> <cn type='integer'> 10 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 75244 </cn> <apply> <power /> <ci> r </ci> <cn type='integer'> 8 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 718317 </cn> <apply> <power /> <ci> r </ci> <cn type='integer'> 6 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 153312 </cn> <apply> <power /> <ci> r </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 4883287 </cn> <apply> <power /> <ci> r </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> 1329084 </cn> </apply> <apply> <sin /> <apply> <times /> <ci> r </ci> <ci> z </ci> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <power /> <apply> <plus /> <ci> r </ci> <cn type='integer'> -3 </cn> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <ci> r </ci> <cn type='integer'> -2 </cn> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <ci> r </ci> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> 6 </cn> </apply> <apply> <power /> <apply> <plus /> <ci> r </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 6 </cn> </apply> <apply> <power /> <apply> <plus /> <ci> r </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <ci> r </ci> <cn type='integer'> 3 </cn> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 15 </cn> <apply> <plus /> <apply> <power /> <ci> r </ci> <cn type='integer'> 10 </cn> </apply> <apply> <times /> <cn type='integer'> 3 </cn> <apply> <power /> <ci> r </ci> <cn type='integer'> 9 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 53 </cn> <apply> <power /> <ci> r </ci> <cn type='integer'> 8 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 69 </cn> <apply> <power /> <ci> r </ci> <cn type='integer'> 7 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 145 </cn> <apply> <power /> <ci> r </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 8211 </cn> <apply> <power /> <ci> r </ci> <cn type='integer'> 5 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 16879 </cn> <apply> <power /> <ci> r </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 32025 </cn> <apply> <power /> <ci> r </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 32954 </cn> <apply> <power /> <ci> r </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 16404 </cn> <ci> r </ci> </apply> </apply> <cn type='integer'> 71528 </cn> </apply> <apply> <sin /> <apply> <times /> <apply> <plus /> <ci> r </ci> <cn type='integer'> 4 </cn> </apply> <ci> z </ci> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <power /> <apply> <plus /> <ci> r </ci> <cn type='integer'> -2 </cn> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <ci> r </ci> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> 4 </cn> </apply> <apply> <power /> <apply> <plus /> <ci> r </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 5 </cn> </apply> <apply> <power /> <apply> <plus /> <ci> r </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> 3 </cn> </apply> <apply> <plus /> <ci> r </ci> <cn type='integer'> 3 </cn> </apply> <apply> <plus /> <ci> r </ci> <cn type='integer'> 4 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 6 </cn> <apply> <plus /> <apply> <power /> <ci> r </ci> <cn type='integer'> 3 </cn> </apply> <apply> <power /> <ci> r </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 31 </cn> <ci> r </ci> </apply> </apply> <cn type='integer'> 89 </cn> </apply> <apply> <sin /> <apply> <times /> <apply> <plus /> <ci> r </ci> <cn type='integer'> 8 </cn> </apply> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <power /> <apply> <plus /> <ci> r </ci> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <ci> r </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 3 </cn> </apply> <apply> <plus /> <ci> r </ci> <cn type='integer'> 2 </cn> </apply> <apply> <plus /> <ci> r </ci> <cn type='integer'> 3 </cn> </apply> <apply> <plus /> <ci> r </ci> <cn type='integer'> 4 </cn> </apply> <apply> <plus /> <ci> r </ci> <cn type='integer'> 5 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <apply> <sin /> <apply> <times /> <apply> <plus /> <ci> r </ci> <cn type='integer'> 12 </cn> </apply> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <plus /> <ci> r </ci> <cn type='integer'> 1 </cn> </apply> <apply> <plus /> <ci> r </ci> <cn type='integer'> 2 </cn> </apply> <apply> <plus /> <ci> r </ci> <cn type='integer'> 3 </cn> </apply> <apply> <plus /> <ci> r </ci> <cn type='integer'> 4 </cn> </apply> <apply> <plus /> <ci> r </ci> <cn type='integer'> 5 </cn> </apply> <apply> <plus /> <ci> r </ci> <cn type='integer'> 6 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <ci> q </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <ci> O </ci> <apply> <power /> <ci> q </ci> <cn type='integer'> 7 </cn> </apply> </apply> </apply> </apply> <apply> <not /> <apply> <and /> <apply> <in /> <ci> r </ci> <integers /> </apply> <apply> <leq /> <cn type='integer'> -6 </cn> <ci> r </ci> <cn type='integer'> 6 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["MathieuS", "[", RowBox[List[RowBox[List["MathieuCharacteristicB", "[", RowBox[List["r_", ",", "q_"]], "]"]], ",", "q_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["Sin", "[", RowBox[List["r", " ", "z"]], "]"]], "+", RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List[FractionBox[RowBox[List["Sin", "[", RowBox[List[RowBox[List["(", RowBox[List["r", "-", "2"]], ")"]], " ", "z"]], "]"]], RowBox[List["r", "-", "1"]]], "-", FractionBox[RowBox[List["Sin", "[", RowBox[List[RowBox[List["(", RowBox[List["r", "+", "2"]], ")"]], " ", "z"]], "]"]], RowBox[List["r", "+", "1"]]]]], ")"]], " ", "q"]], "+", RowBox[List[FractionBox["1", "32"], " ", RowBox[List["(", RowBox[List[FractionBox[RowBox[List["Sin", "[", RowBox[List[RowBox[List["(", RowBox[List["r", "-", "4"]], ")"]], " ", "z"]], "]"]], RowBox[List[RowBox[List["(", RowBox[List["r", "-", "2"]], ")"]], " ", RowBox[List["(", RowBox[List["r", "-", "1"]], ")"]]]]], "-", FractionBox[RowBox[List["2", " ", RowBox[List["(", RowBox[List[SuperscriptBox["r", "2"], "+", "1"]], ")"]], " ", RowBox[List["Sin", "[", RowBox[List["r", " ", "z"]], "]"]]]], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["r", "-", "1"]], ")"]], "2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["r", "+", "1"]], ")"]], "2"]]]], "+", FractionBox[RowBox[List["Sin", "[", RowBox[List[RowBox[List["(", RowBox[List["r", "+", "4"]], ")"]], " ", "z"]], "]"]], RowBox[List[RowBox[List["(", RowBox[List["r", "+", "1"]], ")"]], " ", RowBox[List["(", RowBox[List["r", "+", "2"]], ")"]]]]]]], ")"]], " ", SuperscriptBox["q", "2"]]], "+", RowBox[List[FractionBox["1", "384"], " ", RowBox[List["(", RowBox[List[FractionBox[RowBox[List["Sin", "[", RowBox[List[RowBox[List["(", RowBox[List["r", "-", "6"]], ")"]], " ", "z"]], "]"]], RowBox[List[RowBox[List["(", RowBox[List["r", "-", "3"]], ")"]], " ", RowBox[List["(", RowBox[List["r", "-", "2"]], ")"]], " ", RowBox[List["(", RowBox[List["r", "-", "1"]], ")"]]]]], "-", FractionBox[RowBox[List["3", " ", RowBox[List["(", RowBox[List[SuperscriptBox["r", "3"], "-", SuperscriptBox["r", "2"], "-", "r", "-", "11"]], ")"]], " ", RowBox[List["Sin", "[", RowBox[List[RowBox[List["(", RowBox[List["r", "-", "2"]], ")"]], " ", "z"]], "]"]]]], RowBox[List[RowBox[List["(", RowBox[List["r", "-", "2"]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["r", "-", "1"]], ")"]], "3"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["r", "+", "1"]], ")"]], "2"]]]], "+", FractionBox[RowBox[List["3", " ", RowBox[List["(", RowBox[List[SuperscriptBox["r", "3"], "+", SuperscriptBox["r", "2"], "-", "r", "+", "11"]], ")"]], " ", RowBox[List["Sin", "[", RowBox[List[RowBox[List["(", RowBox[List["r", "+", "2"]], ")"]], " ", "z"]], "]"]]]], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["r", "-", "1"]], ")"]], "2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["r", "+", "1"]], ")"]], "3"], " ", RowBox[List["(", RowBox[List["r", "+", "2"]], ")"]]]]], "-", FractionBox[RowBox[List["Sin", "[", RowBox[List[RowBox[List["(", RowBox[List["r", "+", "6"]], ")"]], " ", "z"]], "]"]], RowBox[List[RowBox[List["(", RowBox[List["r", "+", "1"]], ")"]], " ", RowBox[List["(", RowBox[List["r", "+", "2"]], ")"]], " ", RowBox[List["(", RowBox[List["r", "+", "3"]], ")"]]]]]]], ")"]], " ", SuperscriptBox["q", "3"]]], "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[FractionBox[RowBox[List["Sin", "[", RowBox[List[RowBox[List["(", RowBox[List["r", "-", "8"]], ")"]], " ", "z"]], "]"]], RowBox[List[RowBox[List["(", RowBox[List["r", "-", "4"]], ")"]], " ", RowBox[List["(", RowBox[List["r", "-", "3"]], ")"]], " ", RowBox[List["(", RowBox[List["r", "-", "2"]], ")"]], " ", RowBox[List["(", RowBox[List["r", "-", "1"]], ")"]]]]], "-", FractionBox[RowBox[List["4", " ", RowBox[List["(", RowBox[List[SuperscriptBox["r", "3"], "-", SuperscriptBox["r", "2"], "-", RowBox[List["7", " ", "r"]], "-", "29"]], ")"]], " ", RowBox[List["Sin", "[", RowBox[List[RowBox[List["(", RowBox[List["r", "-", "4"]], ")"]], " ", "z"]], "]"]]]], RowBox[List[RowBox[List["(", RowBox[List["r", "-", "3"]], ")"]], " ", RowBox[List["(", RowBox[List["r", "-", "2"]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["r", "-", "1"]], ")"]], "3"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["r", "+", "1"]], ")"]], "2"]]]], "+", FractionBox[RowBox[List["6", " ", RowBox[List["(", RowBox[List[SuperscriptBox["r", "8"], "-", RowBox[List["15", " ", SuperscriptBox["r", "6"]]], "-", RowBox[List["185", " ", SuperscriptBox["r", "4"]]], "+", RowBox[List["675", " ", SuperscriptBox["r", "2"]]], "+", "316"]], ")"]], " ", RowBox[List["Sin", "[", RowBox[List["r", " ", "z"]], "]"]]]], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["r", "-", "2"]], ")"]], "2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["r", "-", "1"]], ")"]], "4"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["r", "+", "1"]], ")"]], "4"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["r", "+", "2"]], ")"]], "2"]]]], "-", FractionBox[RowBox[List["4", " ", RowBox[List["(", RowBox[List[SuperscriptBox["r", "3"], "+", SuperscriptBox["r", "2"], "-", RowBox[List["7", " ", "r"]], "+", "29"]], ")"]], " ", RowBox[List["Sin", "[", RowBox[List[RowBox[List["(", RowBox[List["r", "+", "4"]], ")"]], " ", "z"]], "]"]]]], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["r", "-", "1"]], ")"]], "2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["r", "+", "1"]], ")"]], "3"], " ", RowBox[List["(", RowBox[List["r", "+", "2"]], ")"]], " ", RowBox[List["(", RowBox[List["r", "+", "3"]], ")"]]]]], "+", FractionBox[RowBox[List["Sin", "[", RowBox[List[RowBox[List["(", RowBox[List["r", "+", "8"]], ")"]], " ", "z"]], "]"]], RowBox[List[RowBox[List["(", RowBox[List["r", "+", "1"]], ")"]], " ", RowBox[List["(", RowBox[List["r", "+", "2"]], ")"]], " ", RowBox[List["(", RowBox[List["r", "+", "3"]], ")"]], " ", RowBox[List["(", RowBox[List["r", "+", "4"]], ")"]]]]]]], ")"]], " ", SuperscriptBox["q", "4"]]], "6144"], "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[FractionBox[RowBox[List["Sin", "[", RowBox[List[RowBox[List["(", RowBox[List["r", "-", "10"]], ")"]], " ", "z"]], "]"]], RowBox[List[RowBox[List["(", RowBox[List["r", "-", "5"]], ")"]], " ", RowBox[List["(", RowBox[List["r", "-", "4"]], ")"]], " ", RowBox[List["(", RowBox[List["r", "-", "3"]], ")"]], " ", RowBox[List["(", RowBox[List["r", "-", "2"]], ")"]], " ", RowBox[List["(", RowBox[List["r", "-", "1"]], ")"]]]]], "-", FractionBox[RowBox[List["5", " ", RowBox[List["(", RowBox[List[SuperscriptBox["r", "3"], "-", SuperscriptBox["r", "2"], "-", RowBox[List["17", " ", "r"]], "-", "55"]], ")"]], " ", RowBox[List["Sin", "[", RowBox[List[RowBox[List["(", RowBox[List["r", "-", "6"]], ")"]], " ", "z"]], "]"]]]], RowBox[List[RowBox[List["(", RowBox[List["r", "-", "4"]], ")"]], " ", RowBox[List["(", RowBox[List["r", "-", "3"]], ")"]], " ", RowBox[List["(", RowBox[List["r", "-", "2"]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["r", "-", "1"]], ")"]], "3"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["r", "+", "1"]], ")"]], "2"]]]], "+", FractionBox[RowBox[List["10", " ", RowBox[List["(", RowBox[List[SuperscriptBox["r", "9"], "-", SuperscriptBox["r", "8"], "-", RowBox[List["31", " ", SuperscriptBox["r", "7"]]], "-", RowBox[List["5", " ", SuperscriptBox["r", "6"]]], "-", RowBox[List["273", " ", SuperscriptBox["r", "5"]]], "+", RowBox[List["2457", " ", SuperscriptBox["r", "4"]]], "+", RowBox[List["1931", " ", SuperscriptBox["r", "3"]]], "-", RowBox[List["6335", " ", SuperscriptBox["r", "2"]]], "-", RowBox[List["3572", " ", "r"]], "-", "7564"]], ")"]], " ", RowBox[List["Sin", "[", RowBox[List[RowBox[List["(", RowBox[List["r", "-", "2"]], ")"]], " ", "z"]], "]"]]]], RowBox[List[RowBox[List["(", RowBox[List["r", "-", "3"]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["r", "-", "2"]], ")"]], "2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["r", "-", "1"]], ")"]], "5"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["r", "+", "1"]], ")"]], "4"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["r", "+", "2"]], ")"]], "2"]]]], "-", FractionBox[RowBox[List["10", " ", RowBox[List["(", RowBox[List[SuperscriptBox["r", "9"], "+", SuperscriptBox["r", "8"], "-", RowBox[List["31", " ", SuperscriptBox["r", "7"]]], "+", RowBox[List["5", " ", SuperscriptBox["r", "6"]]], "-", RowBox[List["273", " ", SuperscriptBox["r", "5"]]], "-", RowBox[List["2457", " ", SuperscriptBox["r", "4"]]], "+", RowBox[List["1931", " ", SuperscriptBox["r", "3"]]], "+", RowBox[List["6335", " ", SuperscriptBox["r", "2"]]], "-", RowBox[List["3572", " ", "r"]], "+", "7564"]], ")"]], " ", RowBox[List["Sin", "[", RowBox[List[RowBox[List["(", RowBox[List["r", "+", "2"]], ")"]], " ", "z"]], "]"]]]], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["r", "-", "2"]], ")"]], "2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["r", "-", "1"]], ")"]], "4"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["r", "+", "1"]], ")"]], "5"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["r", "+", "2"]], ")"]], "2"], " ", RowBox[List["(", RowBox[List["r", "+", "3"]], ")"]]]]], "+", FractionBox[RowBox[List["5", " ", RowBox[List["(", RowBox[List[SuperscriptBox["r", "3"], "+", SuperscriptBox["r", "2"], "-", RowBox[List["17", " ", "r"]], "+", "55"]], ")"]], " ", RowBox[List["Sin", "[", RowBox[List[RowBox[List["(", RowBox[List["r", "+", "6"]], ")"]], " ", "z"]], "]"]]]], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["r", "-", "1"]], ")"]], "2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["r", "+", "1"]], ")"]], "3"], " ", RowBox[List["(", RowBox[List["r", "+", "2"]], ")"]], " ", RowBox[List["(", RowBox[List["r", "+", "3"]], ")"]], " ", RowBox[List["(", RowBox[List["r", "+", "4"]], ")"]]]]], "-", FractionBox[RowBox[List["Sin", "[", RowBox[List[RowBox[List["(", RowBox[List["r", "+", "10"]], ")"]], " ", "z"]], "]"]], RowBox[List[RowBox[List["(", RowBox[List["r", "+", "1"]], ")"]], " ", RowBox[List["(", RowBox[List["r", "+", "2"]], ")"]], " ", RowBox[List["(", RowBox[List["r", "+", "3"]], ")"]], " ", RowBox[List["(", RowBox[List["r", "+", "4"]], ")"]], " ", RowBox[List["(", RowBox[List["r", "+", "5"]], ")"]]]]]]], ")"]], " ", SuperscriptBox["q", "5"]]], "122880"], "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[FractionBox[RowBox[List["Sin", "[", RowBox[List[RowBox[List["(", RowBox[List["r", "-", "12"]], ")"]], " ", "z"]], "]"]], RowBox[List[RowBox[List["(", RowBox[List["r", "-", "6"]], ")"]], " ", RowBox[List["(", RowBox[List["r", "-", "5"]], ")"]], " ", RowBox[List["(", RowBox[List["r", "-", "4"]], ")"]], " ", RowBox[List["(", RowBox[List["r", "-", "3"]], ")"]], " ", RowBox[List["(", RowBox[List["r", "-", "2"]], ")"]], " ", RowBox[List["(", RowBox[List["r", "-", "1"]], ")"]]]]], "-", FractionBox[RowBox[List["6", " ", RowBox[List["(", RowBox[List[SuperscriptBox["r", "3"], "-", SuperscriptBox["r", "2"], "-", RowBox[List["31", " ", "r"]], "-", "89"]], ")"]], " ", RowBox[List["Sin", "[", RowBox[List[RowBox[List["(", RowBox[List["r", "-", "8"]], ")"]], " ", "z"]], "]"]]]], RowBox[List[RowBox[List["(", RowBox[List["r", "-", "5"]], ")"]], " ", RowBox[List["(", RowBox[List["r", "-", "4"]], ")"]], " ", RowBox[List["(", RowBox[List["r", "-", "3"]], ")"]], " ", RowBox[List["(", RowBox[List["r", "-", "2"]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["r", "-", "1"]], ")"]], "3"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["r", "+", "1"]], ")"]], "2"]]]], "+", FractionBox[RowBox[List["15", " ", RowBox[List["(", RowBox[List[SuperscriptBox["r", "10"], "-", RowBox[List["3", " ", SuperscriptBox["r", "9"]]], "-", RowBox[List["53", " ", SuperscriptBox["r", "8"]]], "+", RowBox[List["69", " ", SuperscriptBox["r", "7"]]], "+", RowBox[List["145", " ", SuperscriptBox["r", "6"]]], "+", RowBox[List["8211", " ", SuperscriptBox["r", "5"]]], "-", RowBox[List["16879", " ", SuperscriptBox["r", "4"]]], "-", RowBox[List["32025", " ", SuperscriptBox["r", "3"]]], "+", RowBox[List["32954", " ", SuperscriptBox["r", "2"]]], "+", RowBox[List["16404", " ", "r"]], "+", "71528"]], ")"]], " ", RowBox[List["Sin", "[", RowBox[List[RowBox[List["(", RowBox[List["r", "-", "4"]], ")"]], " ", "z"]], "]"]]]], RowBox[List[RowBox[List["(", RowBox[List["r", "-", "4"]], ")"]], " ", RowBox[List["(", RowBox[List["r", "-", "3"]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["r", "-", "2"]], ")"]], "3"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["r", "-", "1"]], ")"]], "5"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["r", "+", "1"]], ")"]], "4"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["r", "+", "2"]], ")"]], "2"]]]], "-", FractionBox[RowBox[List["20", " ", RowBox[List["(", RowBox[List[SuperscriptBox["r", "14"], "-", RowBox[List["72", " ", SuperscriptBox["r", "12"]]], "+", RowBox[List["597", " ", SuperscriptBox["r", "10"]]], "+", RowBox[List["75244", " ", SuperscriptBox["r", "8"]]], "-", RowBox[List["718317", " ", SuperscriptBox["r", "6"]]], "+", RowBox[List["153312", " ", SuperscriptBox["r", "4"]]], "+", RowBox[List["4883287", " ", SuperscriptBox["r", "2"]]], "+", "1329084"]], ")"]], " ", RowBox[List["Sin", "[", RowBox[List["r", " ", "z"]], "]"]]]], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["r", "-", "3"]], ")"]], "2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["r", "-", "2"]], ")"]], "2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["r", "-", "1"]], ")"]], "6"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["r", "+", "1"]], ")"]], "6"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["r", "+", "2"]], ")"]], "2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["r", "+", "3"]], ")"]], "2"]]]], "+", FractionBox[RowBox[List["15", " ", RowBox[List["(", RowBox[List[SuperscriptBox["r", "10"], "+", RowBox[List["3", " ", SuperscriptBox["r", "9"]]], "-", RowBox[List["53", " ", SuperscriptBox["r", "8"]]], "-", RowBox[List["69", " ", SuperscriptBox["r", "7"]]], "+", RowBox[List["145", " ", SuperscriptBox["r", "6"]]], "-", RowBox[List["8211", " ", SuperscriptBox["r", "5"]]], "-", RowBox[List["16879", " ", SuperscriptBox["r", "4"]]], "+", RowBox[List["32025", " ", SuperscriptBox["r", "3"]]], "+", RowBox[List["32954", " ", SuperscriptBox["r", "2"]]], "-", RowBox[List["16404", " ", "r"]], "+", "71528"]], ")"]], " ", RowBox[List["Sin", "[", RowBox[List[RowBox[List["(", RowBox[List["r", "+", "4"]], ")"]], " ", "z"]], "]"]]]], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["r", "-", "2"]], ")"]], "2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["r", "-", "1"]], ")"]], "4"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["r", "+", "1"]], ")"]], "5"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["r", "+", "2"]], ")"]], "3"], " ", RowBox[List["(", RowBox[List["r", "+", "3"]], ")"]], " ", RowBox[List["(", RowBox[List["r", "+", "4"]], ")"]]]]], "-", FractionBox[RowBox[List["6", " ", RowBox[List["(", RowBox[List[SuperscriptBox["r", "3"], "+", SuperscriptBox["r", "2"], "-", RowBox[List["31", " ", "r"]], "+", "89"]], ")"]], " ", RowBox[List["Sin", "[", RowBox[List[RowBox[List["(", RowBox[List["r", "+", "8"]], ")"]], " ", "z"]], "]"]]]], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["r", "-", "1"]], ")"]], "2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["r", "+", "1"]], ")"]], "3"], " ", RowBox[List["(", RowBox[List["r", "+", "2"]], ")"]], " ", RowBox[List["(", RowBox[List["r", "+", "3"]], ")"]], " ", RowBox[List["(", RowBox[List["r", "+", "4"]], ")"]], " ", RowBox[List["(", RowBox[List["r", "+", "5"]], ")"]]]]], "+", FractionBox[RowBox[List["Sin", "[", RowBox[List[RowBox[List["(", RowBox[List["r", "+", "12"]], ")"]], " ", "z"]], "]"]], RowBox[List[RowBox[List["(", RowBox[List["r", "+", "1"]], ")"]], " ", RowBox[List["(", RowBox[List["r", "+", "2"]], ")"]], " ", RowBox[List["(", RowBox[List["r", "+", "3"]], ")"]], " ", RowBox[List["(", RowBox[List["r", "+", "4"]], ")"]], " ", RowBox[List["(", RowBox[List["r", "+", "5"]], ")"]], " ", RowBox[List["(", RowBox[List["r", "+", "6"]], ")"]]]]]]], ")"]], " ", SuperscriptBox["q", "6"]]], "2949120"], "+", SuperscriptBox[RowBox[List["O", "[", "q", "]"]], "7"]]], "/;", RowBox[List["!", RowBox[List["(", RowBox[List[RowBox[List["r", "\[Element]", "Integers"]], "&&", RowBox[List[RowBox[List["-", "6"]], "\[LessEqual]", "r", "\[LessEqual]", "6"]]]], ")"]]]]]]]]]]


Date Added to functions.wolfram.com (modification date)





2001-10-29