Wolfram Researchfunctions.wolfram.comOther Wolfram Sites
Search Site
Function CategoriesGraphics GalleryNotationsGeneral IdentitiesAbout This Site ContributeEmail CommentsSign the Guestbook

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
 











MathieuCharacteristicB






Mathematica Notation

Traditional Notation









Mathieu and Spheroidal Functions > MathieuCharacteristicB[r,q] > Series representations > Generalized power series > Expansions at q==0





http://functions.wolfram.com/11.06.06.0001.01









  


  










Input Form





MathieuCharacteristicB[r, q] \[Proportional] SeriesData[$CellContext`q, 0, {$CellContext`r^2, 0, Rational[1, 2]/((-1 + $CellContext`r) (1 + $CellContext`r)), 0, (Rational[1, 32] (7 + 5 $CellContext`r^2))/ ((-2 + $CellContext`r) (-1 + $CellContext`r)^3 (1 + $CellContext`r)^3 (2 + $CellContext`r)), 0, (Rational[1, 64] (29 + 58 $CellContext`r^2 + 9 $CellContext`r^4))/((-3 + $CellContext`r) (-2 + $CellContext`r) (-1 + $CellContext`r)^5 (1 + $CellContext`r)^5 (2 + $CellContext`r) (3 + $CellContext`r)), 0, (Rational[1, 8192] (274748 + 827565 $CellContext`r^2 + 64228 $CellContext`r^4 - 140354 $CellContext`r^6 + 9144 $CellContext`r^8 + 1469 $CellContext`r^10))/ ((-4 + $CellContext`r) (-3 + $CellContext`r) (-2 + $CellContext`r)^3 (-1 + $CellContext`r)^7 (1 + $CellContext`r)^7 (2 + $CellContext`r)^3 (3 + $CellContext`r) (4 + $CellContext`r)), 0, (Rational[1, 16384] (4453452 + 20651309 $CellContext`r^2 + 13541915 $CellContext`r^4 - 2844430 $CellContext`r^6 - 1039598 $CellContext`r^8 + 69361 $CellContext`r^10 + 4471 $CellContext`r^12))/((-5 + $CellContext`r) (-4 + $CellContext`r) (-3 + $CellContext`r) (-2 + $CellContext`r)^3 (-1 + $CellContext`r)^9 (1 + $CellContext`r)^9 (2 + $CellContext`r)^3 (3 + $CellContext`r) (4 + $CellContext`r) (5 + $CellContext`r))}, 0, 11, 1] /; !(Element[r, Integers] && -10 <= r <= 10)










Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["MathieuCharacteristicB", "[", RowBox[List["r", ",", "q"]], "]"]], "\[Proportional]", InterpretationBox[RowBox[List[SuperscriptBox["r", "2"], "+", FractionBox[SuperscriptBox["q", "2"], RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "r"]], ")"]], " ", RowBox[List["(", RowBox[List["1", "+", "r"]], ")"]]]]], "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["7", "+", RowBox[List["5", " ", SuperscriptBox["r", "2"]]]]], ")"]], " ", SuperscriptBox["q", "4"]]], RowBox[List["32", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "2"]], "+", "r"]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "r"]], ")"]], "3"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", "r"]], ")"]], "3"], " ", RowBox[List["(", RowBox[List["2", "+", "r"]], ")"]]]]], "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["29", "+", RowBox[List["58", " ", SuperscriptBox["r", "2"]]], "+", RowBox[List["9", " ", SuperscriptBox["r", "4"]]]]], ")"]], " ", SuperscriptBox["q", "6"]]], RowBox[List["64", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "3"]], "+", "r"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "2"]], "+", "r"]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "r"]], ")"]], "5"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", "r"]], ")"]], "5"], " ", RowBox[List["(", RowBox[List["2", "+", "r"]], ")"]], " ", RowBox[List["(", RowBox[List["3", "+", "r"]], ")"]]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["274748", "+", RowBox[List["827565", " ", SuperscriptBox["r", "2"]]], "+", RowBox[List["64228", " ", SuperscriptBox["r", "4"]]], "-", RowBox[List["140354", " ", SuperscriptBox["r", "6"]]], "+", RowBox[List["9144", " ", SuperscriptBox["r", "8"]]], "+", RowBox[List["1469", " ", SuperscriptBox["r", "10"]]]]], ")"]], " ", SuperscriptBox["q", "8"]]], ")"]], "/", RowBox[List["(", RowBox[List["8192", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "4"]], "+", "r"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "3"]], "+", "r"]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "2"]], "+", "r"]], ")"]], "3"], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "r"]], ")"]], "7"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", "r"]], ")"]], "7"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["2", "+", "r"]], ")"]], "3"], " ", RowBox[List["(", RowBox[List["3", "+", "r"]], ")"]], " ", RowBox[List["(", RowBox[List["4", "+", "r"]], ")"]]]], ")"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["4453452", "+", RowBox[List["20651309", " ", SuperscriptBox["r", "2"]]], "+", RowBox[List["13541915", " ", SuperscriptBox["r", "4"]]], "-", RowBox[List["2844430", " ", SuperscriptBox["r", "6"]]], "-", RowBox[List["1039598", " ", SuperscriptBox["r", "8"]]], "+", RowBox[List["69361", " ", SuperscriptBox["r", "10"]]], "+", RowBox[List["4471", " ", SuperscriptBox["r", "12"]]]]], ")"]], " ", SuperscriptBox["q", "10"]]], ")"]], "/", RowBox[List["(", RowBox[List["16384", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "5"]], "+", "r"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "4"]], "+", "r"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "3"]], "+", "r"]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "2"]], "+", "r"]], ")"]], "3"], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "r"]], ")"]], "9"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", "r"]], ")"]], "9"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["2", "+", "r"]], ")"]], "3"], " ", RowBox[List["(", RowBox[List["3", "+", "r"]], ")"]], " ", RowBox[List["(", RowBox[List["4", "+", "r"]], ")"]], " ", RowBox[List["(", RowBox[List["5", "+", "r"]], ")"]]]], ")"]]]], "+", InterpretationBox[SuperscriptBox[RowBox[List["O", "[", "q", "]"]], "11"], SeriesData[$CellContext`q, 0, List[], 0, 11, 1]]]], SeriesData[$CellContext`q, 0, List[Power[$CellContext`r, 2], 0, Times[Rational[1, 2], Power[Plus[-1, $CellContext`r], -1], Power[Plus[1, $CellContext`r], -1]], 0, Times[Rational[1, 32], Power[Plus[-2, $CellContext`r], -1], Power[Plus[-1, $CellContext`r], -3], Power[Plus[1, $CellContext`r], -3], Power[Plus[2, $CellContext`r], -1], Plus[7, Times[5, Power[$CellContext`r, 2]]]], 0, Times[Rational[1, 64], Power[Plus[-3, $CellContext`r], -1], Power[Plus[-2, $CellContext`r], -1], Power[Plus[-1, $CellContext`r], -5], Power[Plus[1, $CellContext`r], -5], Power[Plus[2, $CellContext`r], -1], Power[Plus[3, $CellContext`r], -1], Plus[29, Times[58, Power[$CellContext`r, 2]], Times[9, Power[$CellContext`r, 4]]]], 0, Times[Rational[1, 8192], Power[Plus[-4, $CellContext`r], -1], Power[Plus[-3, $CellContext`r], -1], Power[Plus[-2, $CellContext`r], -3], Power[Plus[-1, $CellContext`r], -7], Power[Plus[1, $CellContext`r], -7], Power[Plus[2, $CellContext`r], -3], Power[Plus[3, $CellContext`r], -1], Power[Plus[4, $CellContext`r], -1], Plus[274748, Times[827565, Power[$CellContext`r, 2]], Times[64228, Power[$CellContext`r, 4]], Times[-1, 140354, Power[$CellContext`r, 6]], Times[9144, Power[$CellContext`r, 8]], Times[1469, Power[$CellContext`r, 10]]]], 0, Times[Rational[1, 16384], Power[Plus[-5, $CellContext`r], -1], Power[Plus[-4, $CellContext`r], -1], Power[Plus[-3, $CellContext`r], -1], Power[Plus[-2, $CellContext`r], -3], Power[Plus[-1, $CellContext`r], -9], Power[Plus[1, $CellContext`r], -9], Power[Plus[2, $CellContext`r], -3], Power[Plus[3, $CellContext`r], -1], Power[Plus[4, $CellContext`r], -1], Power[Plus[5, $CellContext`r], -1], Plus[4453452, Times[20651309, Power[$CellContext`r, 2]], Times[13541915, Power[$CellContext`r, 4]], Times[-1, 2844430, Power[$CellContext`r, 6]], Times[-1, 1039598, Power[$CellContext`r, 8]], Times[69361, Power[$CellContext`r, 10]], Times[4471, Power[$CellContext`r, 12]]]]], 0, 11, 1]]]], "/;", RowBox[List["Not", "[", RowBox[List[RowBox[List["r", "\[Element]", "Integers"]], "\[And]", RowBox[List[RowBox[List["-", "10"]], "\[LessEqual]", "r", "\[LessEqual]", "10"]]]], "]"]]]]]]










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> <msub> <semantics> <mi> b </mi> <annotation-xml encoding='MathML-Content'> <ci> MathieuCharacteristicB </ci> </annotation-xml> </semantics> <mi> r </mi> </msub> <mo> ( </mo> <mi> q </mi> <mo> ) </mo> </mrow> <mo> &#8733; </mo> <semantics> <mrow> <msup> <mi> r </mi> <mn> 2 </mn> </msup> <mo> + </mo> <mfrac> <msup> <mi> q </mi> <mn> 2 </mn> </msup> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <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> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> <mo> + </mo> <mfrac> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 5 </mn> <mo> &#8290; </mo> <msup> <mi> r </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mn> 7 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 4 </mn> </msup> </mrow> <mrow> <mn> 32 </mn> <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> 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> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 9 </mn> <mo> &#8290; </mo> <msup> <mi> r </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 58 </mn> <mo> &#8290; </mo> <msup> <mi> r </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mn> 29 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 6 </mn> </msup> </mrow> <mrow> <mn> 64 </mn> <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> 5 </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> <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> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 1469 </mn> <mo> &#8290; </mo> <msup> <mi> r </mi> <mn> 10 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 9144 </mn> <mo> &#8290; </mo> <msup> <mi> r </mi> <mn> 8 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 140354 </mn> <mo> &#8290; </mo> <msup> <mi> r </mi> <mn> 6 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 64228 </mn> <mo> &#8290; </mo> <msup> <mi> r </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 827565 </mn> <mo> &#8290; </mo> <msup> <mi> r </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mn> 274748 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 8 </mn> </msup> </mrow> <mrow> <mn> 8192 </mn> <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> <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> 7 </mn> </msup> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 7 </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> </mfrac> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 4471 </mn> <mo> &#8290; </mo> <msup> <mi> r </mi> <mn> 12 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 69361 </mn> <mo> &#8290; </mo> <msup> <mi> r </mi> <mn> 10 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 1039598 </mn> <mo> &#8290; </mo> <msup> <mi> r </mi> <mn> 8 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 2844430 </mn> <mo> &#8290; </mo> <msup> <mi> r </mi> <mn> 6 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 13541915 </mn> <mo> &#8290; </mo> <msup> <mi> r </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 20651309 </mn> <mo> &#8290; </mo> <msup> <mi> r </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mn> 4453452 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 10 </mn> </msup> </mrow> <mo> ) </mo> </mrow> <mo> / </mo> <mrow> <mo> ( </mo> <mrow> <mn> 16384 </mn> <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> <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> 9 </mn> </msup> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 9 </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> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 5 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mi> O </mi> <mo> &#8289; </mo> <mo> ( </mo> <msup> <mi> q </mi> <mn> 11 </mn> </msup> <mo> ) </mo> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> SeriesData </ci> <ci> $CellContext`q </ci> <cn type='integer'> 0 </cn> <list> <apply> <power /> <ci> $CellContext`r </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> 0 </cn> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <power /> <apply> <plus /> <cn type='integer'> -1 </cn> <ci> $CellContext`r </ci> </apply> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <ci> $CellContext`r </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 0 </cn> <apply> <times /> <cn type='rational'> 1 <sep /> 32 </cn> <apply> <power /> <apply> <plus /> <cn type='integer'> -2 </cn> <ci> $CellContext`r </ci> </apply> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> -1 </cn> <ci> $CellContext`r </ci> </apply> <cn type='integer'> -3 </cn> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <ci> $CellContext`r </ci> </apply> <cn type='integer'> -3 </cn> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> 2 </cn> <ci> $CellContext`r </ci> </apply> <cn type='integer'> -1 </cn> </apply> <apply> <plus /> <cn type='integer'> 7 </cn> <apply> <times /> <cn type='integer'> 5 </cn> <apply> <power /> <ci> $CellContext`r </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </apply> <cn type='integer'> 0 </cn> <apply> <times /> <cn type='rational'> 1 <sep /> 64 </cn> <apply> <power /> <apply> <plus /> <cn type='integer'> -3 </cn> <ci> $CellContext`r </ci> </apply> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> -2 </cn> <ci> $CellContext`r </ci> </apply> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> -1 </cn> <ci> $CellContext`r </ci> </apply> <cn type='integer'> -5 </cn> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <ci> $CellContext`r </ci> </apply> <cn type='integer'> -5 </cn> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> 2 </cn> <ci> $CellContext`r </ci> </apply> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> 3 </cn> <ci> $CellContext`r </ci> </apply> <cn type='integer'> -1 </cn> </apply> <apply> <plus /> <cn type='integer'> 29 </cn> <apply> <times /> <cn type='integer'> 58 </cn> <apply> <power /> <ci> $CellContext`r </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 9 </cn> <apply> <power /> <ci> $CellContext`r </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> </apply> <cn type='integer'> 0 </cn> <apply> <times /> <cn type='rational'> 1 <sep /> 8192 </cn> <apply> <power /> <apply> <plus /> <cn type='integer'> -4 </cn> <ci> $CellContext`r </ci> </apply> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> -3 </cn> <ci> $CellContext`r </ci> </apply> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> -2 </cn> <ci> $CellContext`r </ci> </apply> <cn type='integer'> -3 </cn> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> -1 </cn> <ci> $CellContext`r </ci> </apply> <cn type='integer'> -7 </cn> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <ci> $CellContext`r </ci> </apply> <cn type='integer'> -7 </cn> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> 2 </cn> <ci> $CellContext`r </ci> </apply> <cn type='integer'> -3 </cn> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> 3 </cn> <ci> $CellContext`r </ci> </apply> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> 4 </cn> <ci> $CellContext`r </ci> </apply> <cn type='integer'> -1 </cn> </apply> <apply> <plus /> <cn type='integer'> 274748 </cn> <apply> <times /> <cn type='integer'> 827565 </cn> <apply> <power /> <ci> $CellContext`r </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 64228 </cn> <apply> <power /> <ci> $CellContext`r </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='integer'> 140354 </cn> <apply> <power /> <ci> $CellContext`r </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 9144 </cn> <apply> <power /> <ci> $CellContext`r </ci> <cn type='integer'> 8 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 1469 </cn> <apply> <power /> <ci> $CellContext`r </ci> <cn type='integer'> 10 </cn> </apply> </apply> </apply> </apply> <cn type='integer'> 0 </cn> <apply> <times /> <cn type='rational'> 1 <sep /> 16384 </cn> <apply> <power /> <apply> <plus /> <cn type='integer'> -5 </cn> <ci> $CellContext`r </ci> </apply> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> -4 </cn> <ci> $CellContext`r </ci> </apply> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> -3 </cn> <ci> $CellContext`r </ci> </apply> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> -2 </cn> <ci> $CellContext`r </ci> </apply> <cn type='integer'> -3 </cn> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> -1 </cn> <ci> $CellContext`r </ci> </apply> <cn type='integer'> -9 </cn> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <ci> $CellContext`r </ci> </apply> <cn type='integer'> -9 </cn> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> 2 </cn> <ci> $CellContext`r </ci> </apply> <cn type='integer'> -3 </cn> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> 3 </cn> <ci> $CellContext`r </ci> </apply> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> 4 </cn> <ci> $CellContext`r </ci> </apply> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> 5 </cn> <ci> $CellContext`r </ci> </apply> <cn type='integer'> -1 </cn> </apply> <apply> <plus /> <cn type='integer'> 4453452 </cn> <apply> <times /> <cn type='integer'> 20651309 </cn> <apply> <power /> <ci> $CellContext`r </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 13541915 </cn> <apply> <power /> <ci> $CellContext`r </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='integer'> 2844430 </cn> <apply> <power /> <ci> $CellContext`r </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='integer'> 1039598 </cn> <apply> <power /> <ci> $CellContext`r </ci> <cn type='integer'> 8 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 69361 </cn> <apply> <power /> <ci> $CellContext`r </ci> <cn type='integer'> 10 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 4471 </cn> <apply> <power /> <ci> $CellContext`r </ci> <cn type='integer'> 12 </cn> </apply> </apply> </apply> </apply> </list> <cn type='integer'> 0 </cn> <cn type='integer'> 11 </cn> <cn type='integer'> 1 </cn> </apply> </annotation-xml> </semantics> </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> 10 </mn> </mrow> <mo> &#8804; </mo> <mi> r </mi> <mo> &#8804; </mo> <mn> 10 </mn> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <ci> Proportional </ci> <apply> <ci> MathieuCharacteristicB </ci> <ci> r </ci> <ci> q </ci> </apply> <apply> <ci> SeriesData </ci> <ci> $CellContext`q </ci> <cn type='integer'> 0 </cn> <list> <apply> <power /> <ci> $CellContext`r </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> 0 </cn> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <power /> <apply> <plus /> <cn type='integer'> -1 </cn> <ci> $CellContext`r </ci> </apply> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <ci> $CellContext`r </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 0 </cn> <apply> <times /> <cn type='rational'> 1 <sep /> 32 </cn> <apply> <power /> <apply> <plus /> <cn type='integer'> -2 </cn> <ci> $CellContext`r </ci> </apply> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> -1 </cn> <ci> $CellContext`r </ci> </apply> <cn type='integer'> -3 </cn> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <ci> $CellContext`r </ci> </apply> <cn type='integer'> -3 </cn> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> 2 </cn> <ci> $CellContext`r </ci> </apply> <cn type='integer'> -1 </cn> </apply> <apply> <plus /> <cn type='integer'> 7 </cn> <apply> <times /> <cn type='integer'> 5 </cn> <apply> <power /> <ci> $CellContext`r </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </apply> <cn type='integer'> 0 </cn> <apply> <times /> <cn type='rational'> 1 <sep /> 64 </cn> <apply> <power /> <apply> <plus /> <cn type='integer'> -3 </cn> <ci> $CellContext`r </ci> </apply> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> -2 </cn> <ci> $CellContext`r </ci> </apply> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> -1 </cn> <ci> $CellContext`r </ci> </apply> <cn type='integer'> -5 </cn> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <ci> $CellContext`r </ci> </apply> <cn type='integer'> -5 </cn> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> 2 </cn> <ci> $CellContext`r </ci> </apply> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> 3 </cn> <ci> $CellContext`r </ci> </apply> <cn type='integer'> -1 </cn> </apply> <apply> <plus /> <cn type='integer'> 29 </cn> <apply> <times /> <cn type='integer'> 58 </cn> <apply> <power /> <ci> $CellContext`r </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 9 </cn> <apply> <power /> <ci> $CellContext`r </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> </apply> <cn type='integer'> 0 </cn> <apply> <times /> <cn type='rational'> 1 <sep /> 8192 </cn> <apply> <power /> <apply> <plus /> <cn type='integer'> -4 </cn> <ci> $CellContext`r </ci> </apply> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> -3 </cn> <ci> $CellContext`r </ci> </apply> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> -2 </cn> <ci> $CellContext`r </ci> </apply> <cn type='integer'> -3 </cn> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> -1 </cn> <ci> $CellContext`r </ci> </apply> <cn type='integer'> -7 </cn> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <ci> $CellContext`r </ci> </apply> <cn type='integer'> -7 </cn> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> 2 </cn> <ci> $CellContext`r </ci> </apply> <cn type='integer'> -3 </cn> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> 3 </cn> <ci> $CellContext`r </ci> </apply> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> 4 </cn> <ci> $CellContext`r </ci> </apply> <cn type='integer'> -1 </cn> </apply> <apply> <plus /> <cn type='integer'> 274748 </cn> <apply> <times /> <cn type='integer'> 827565 </cn> <apply> <power /> <ci> $CellContext`r </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 64228 </cn> <apply> <power /> <ci> $CellContext`r </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='integer'> 140354 </cn> <apply> <power /> <ci> $CellContext`r </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 9144 </cn> <apply> <power /> <ci> $CellContext`r </ci> <cn type='integer'> 8 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 1469 </cn> <apply> <power /> <ci> $CellContext`r </ci> <cn type='integer'> 10 </cn> </apply> </apply> </apply> </apply> <cn type='integer'> 0 </cn> <apply> <times /> <cn type='rational'> 1 <sep /> 16384 </cn> <apply> <power /> <apply> <plus /> <cn type='integer'> -5 </cn> <ci> $CellContext`r </ci> </apply> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> -4 </cn> <ci> $CellContext`r </ci> </apply> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> -3 </cn> <ci> $CellContext`r </ci> </apply> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> -2 </cn> <ci> $CellContext`r </ci> </apply> <cn type='integer'> -3 </cn> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> -1 </cn> <ci> $CellContext`r </ci> </apply> <cn type='integer'> -9 </cn> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <ci> $CellContext`r </ci> </apply> <cn type='integer'> -9 </cn> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> 2 </cn> <ci> $CellContext`r </ci> </apply> <cn type='integer'> -3 </cn> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> 3 </cn> <ci> $CellContext`r </ci> </apply> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> 4 </cn> <ci> $CellContext`r </ci> </apply> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> 5 </cn> <ci> $CellContext`r </ci> </apply> <cn type='integer'> -1 </cn> </apply> <apply> <plus /> <cn type='integer'> 4453452 </cn> <apply> <times /> <cn type='integer'> 20651309 </cn> <apply> <power /> <ci> $CellContext`r </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 13541915 </cn> <apply> <power /> <ci> $CellContext`r </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='integer'> 2844430 </cn> <apply> <power /> <ci> $CellContext`r </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='integer'> 1039598 </cn> <apply> <power /> <ci> $CellContext`r </ci> <cn type='integer'> 8 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 69361 </cn> <apply> <power /> <ci> $CellContext`r </ci> <cn type='integer'> 10 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 4471 </cn> <apply> <power /> <ci> $CellContext`r </ci> <cn type='integer'> 12 </cn> </apply> </apply> </apply> </apply> </list> <cn type='integer'> 0 </cn> <cn type='integer'> 11 </cn> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <not /> <apply> <and /> <apply> <in /> <ci> r </ci> <integers /> </apply> <apply> <leq /> <cn type='integer'> -10 </cn> <ci> r </ci> <cn type='integer'> 10 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["MathieuCharacteristicB", "[", RowBox[List["r_", ",", "q_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[InterpretationBox[RowBox[List[SuperscriptBox["$CellContext`r", "2"], "+", FractionBox[RowBox[List[FractionBox["1", "2"], " ", SuperscriptBox["$CellContext`q", "2"]]], RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "$CellContext`r"]], ")"]], " ", RowBox[List["(", RowBox[List["1", "+", "$CellContext`r"]], ")"]]]]], "+", FractionBox[RowBox[List[FractionBox["1", "32"], " ", RowBox[List["(", RowBox[List["7", "+", RowBox[List["5", " ", SuperscriptBox["$CellContext`r", "2"]]]]], ")"]], " ", SuperscriptBox["$CellContext`q", "4"]]], RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "2"]], "+", "$CellContext`r"]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "$CellContext`r"]], ")"]], "3"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", "$CellContext`r"]], ")"]], "3"], " ", RowBox[List["(", RowBox[List["2", "+", "$CellContext`r"]], ")"]]]]], "+", FractionBox[RowBox[List[FractionBox["1", "64"], " ", RowBox[List["(", RowBox[List["29", "+", RowBox[List["58", " ", SuperscriptBox["$CellContext`r", "2"]]], "+", RowBox[List["9", " ", SuperscriptBox["$CellContext`r", "4"]]]]], ")"]], " ", SuperscriptBox["$CellContext`q", "6"]]], RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "3"]], "+", "$CellContext`r"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "2"]], "+", "$CellContext`r"]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "$CellContext`r"]], ")"]], "5"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", "$CellContext`r"]], ")"]], "5"], " ", RowBox[List["(", RowBox[List["2", "+", "$CellContext`r"]], ")"]], " ", RowBox[List["(", RowBox[List["3", "+", "$CellContext`r"]], ")"]]]]], "+", FractionBox[RowBox[List[FractionBox["1", "8192"], " ", RowBox[List["(", RowBox[List["274748", "+", RowBox[List["827565", " ", SuperscriptBox["$CellContext`r", "2"]]], "+", RowBox[List["64228", " ", SuperscriptBox["$CellContext`r", "4"]]], "-", RowBox[List["140354", " ", SuperscriptBox["$CellContext`r", "6"]]], "+", RowBox[List["9144", " ", SuperscriptBox["$CellContext`r", "8"]]], "+", RowBox[List["1469", " ", SuperscriptBox["$CellContext`r", "10"]]]]], ")"]], " ", SuperscriptBox["$CellContext`q", "8"]]], RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "4"]], "+", "$CellContext`r"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "3"]], "+", "$CellContext`r"]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "2"]], "+", "$CellContext`r"]], ")"]], "3"], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "$CellContext`r"]], ")"]], "7"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", "$CellContext`r"]], ")"]], "7"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["2", "+", "$CellContext`r"]], ")"]], "3"], " ", RowBox[List["(", RowBox[List["3", "+", "$CellContext`r"]], ")"]], " ", RowBox[List["(", RowBox[List["4", "+", "$CellContext`r"]], ")"]]]]], "+", FractionBox[RowBox[List[FractionBox["1", "16384"], " ", RowBox[List["(", RowBox[List["4453452", "+", RowBox[List["20651309", " ", SuperscriptBox["$CellContext`r", "2"]]], "+", RowBox[List["13541915", " ", SuperscriptBox["$CellContext`r", "4"]]], "-", RowBox[List["2844430", " ", SuperscriptBox["$CellContext`r", "6"]]], "-", RowBox[List["1039598", " ", SuperscriptBox["$CellContext`r", "8"]]], "+", RowBox[List["69361", " ", SuperscriptBox["$CellContext`r", "10"]]], "+", RowBox[List["4471", " ", SuperscriptBox["$CellContext`r", "12"]]]]], ")"]], " ", SuperscriptBox["$CellContext`q", "10"]]], RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "5"]], "+", "$CellContext`r"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "4"]], "+", "$CellContext`r"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "3"]], "+", "$CellContext`r"]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "2"]], "+", "$CellContext`r"]], ")"]], "3"], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "$CellContext`r"]], ")"]], "9"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", "$CellContext`r"]], ")"]], "9"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["2", "+", "$CellContext`r"]], ")"]], "3"], " ", RowBox[List["(", RowBox[List["3", "+", "$CellContext`r"]], ")"]], " ", RowBox[List["(", RowBox[List["4", "+", "$CellContext`r"]], ")"]], " ", RowBox[List["(", RowBox[List["5", "+", "$CellContext`r"]], ")"]]]]], "+", InterpretationBox[SuperscriptBox[RowBox[List["O", "[", "$CellContext`q", "]"]], "11"], SeriesData[$CellContext`q, 0, List[], 0, 11, 1], Rule[Editable, False]]]], SeriesData[$CellContext`q, 0, List[Power[$CellContext`r, 2], 0, Times[Rational[1, 2], Power[Plus[-1, $CellContext`r], -1], Power[Plus[1, $CellContext`r], -1]], 0, Times[Rational[1, 32], Power[Plus[-2, $CellContext`r], -1], Power[Plus[-1, $CellContext`r], -3], Power[Plus[1, $CellContext`r], -3], Power[Plus[2, $CellContext`r], -1], Plus[7, Times[5, Power[$CellContext`r, 2]]]], 0, Times[Rational[1, 64], Power[Plus[-3, $CellContext`r], -1], Power[Plus[-2, $CellContext`r], -1], Power[Plus[-1, $CellContext`r], -5], Power[Plus[1, $CellContext`r], -5], Power[Plus[2, $CellContext`r], -1], Power[Plus[3, $CellContext`r], -1], Plus[29, Times[58, Power[$CellContext`r, 2]], Times[9, Power[$CellContext`r, 4]]]], 0, Times[Rational[1, 8192], Power[Plus[-4, $CellContext`r], -1], Power[Plus[-3, $CellContext`r], -1], Power[Plus[-2, $CellContext`r], -3], Power[Plus[-1, $CellContext`r], -7], Power[Plus[1, $CellContext`r], -7], Power[Plus[2, $CellContext`r], -3], Power[Plus[3, $CellContext`r], -1], Power[Plus[4, $CellContext`r], -1], Plus[274748, Times[827565, Power[$CellContext`r, 2]], Times[64228, Power[$CellContext`r, 4]], Times[-1, 140354, Power[$CellContext`r, 6]], Times[9144, Power[$CellContext`r, 8]], Times[1469, Power[$CellContext`r, 10]]]], 0, Times[Rational[1, 16384], Power[Plus[-5, $CellContext`r], -1], Power[Plus[-4, $CellContext`r], -1], Power[Plus[-3, $CellContext`r], -1], Power[Plus[-2, $CellContext`r], -3], Power[Plus[-1, $CellContext`r], -9], Power[Plus[1, $CellContext`r], -9], Power[Plus[2, $CellContext`r], -3], Power[Plus[3, $CellContext`r], -1], Power[Plus[4, $CellContext`r], -1], Power[Plus[5, $CellContext`r], -1], Plus[4453452, Times[20651309, Power[$CellContext`r, 2]], Times[13541915, Power[$CellContext`r, 4]], Times[-1, 2844430, Power[$CellContext`r, 6]], Times[-1, 1039598, Power[$CellContext`r, 8]], Times[69361, Power[$CellContext`r, 10]], Times[4471, Power[$CellContext`r, 12]]]]], 0, 11, 1], Rule[Editable, False]], "/;", RowBox[List["!", RowBox[List["(", RowBox[List[RowBox[List["r", "\[Element]", "Integers"]], "&&", RowBox[List[RowBox[List["-", "10"]], "\[LessEqual]", "r", "\[LessEqual]", "10"]]]], ")"]]]]]]]]]]










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





2001-10-29





© 1998-2014 Wolfram Research, Inc.