Even Mathieu function: Series representations (formula 11.01.06.0008)

MathieuC

$Mathematica Notation$

Mathieu and Spheroidal Functions

MathieuC[a,q,z]

Series representations

Generalized power series

Expansions at q==0

http://functions.wolfram.com/11.01.06.0008.01

Input Form

MathieuC[MathieuCharacteristicA[4, q], q, z] \[Proportional] SeriesData[$CellContext`q, 0, {Cos[3 $CellContext`z], Rational[1, 8] Cos[$CellContext`z] + Rational[-1, 16] Cos[5 $CellContext`z], Rational[1, 64] Cos[$CellContext`z] + Rational[-5, 512] Cos[3 $CellContext`z] + Rational[1, 640] Cos[7 $CellContext`z], Rational[-1, 4096] Cos[$CellContext`z] + Rational[-1, 512] Cos[3 $CellContext`z] + Rational[11, 40960] Cos[5 $CellContext`z] + Rational[-1, 46080] Cos[9 $CellContext`z], Rational[-21, 32768] Cos[$CellContext`z] + Rational[-1621, 13107200] Cos[3 $CellContext`z] + Rational[1, 16384] Cos[5 $CellContext`z] + Rational[-11, 2949120] Cos[7 $CellContext`z] + Rational[1, 5160960] Cos[11 $CellContext`z], Rational[-14061, 104857600] Cos[$CellContext`z] + Rational[9, 131072] Cos[3 $CellContext`z] + Rational[12329, 1887436800] Cos[5 $CellContext`z] + Rational[-3, 3276800] Cos[7 $CellContext`z] + Rational[1, 33030144] Cos[9 $CellContext`z] + Rational[-1, 825753600] Cos[13 $CellContext`z], Rational[699, 838860800] Cos[$CellContext`z] + Rational[13050583, 543581798400] Cos[3 $CellContext`z] + Rational[-533, 209715200] Cos[5 $CellContext`z] + Rational[-76679, 528482304000] Cos[7 $CellContext`z] + Rational[17, 2123366400] Cos[9 $CellContext`z] + Rational[-1, 6606028800] Cos[11 $CellContext`z] + Rational[1, 178362777600] Cos[15 $CellContext`z], Rational[31826419, 4348654387200] Cos[$CellContext`z] + Rational[70123, 33554432000] Cos[3 $CellContext`z] + Rational[-326021051, 304405807104000] Cos[5 $CellContext`z] + Rational[1319, 27179089920] Cos[7 $CellContext`z] + Rational[7831, 4227858432000] Cos[9 $CellContext`z] + Rational[-37, 832359628800] Cos[11 $CellContext`z] + Rational[1, 2283043553280] Cos[13 $CellContext`z] + Rational[-1, 49941577728000] Cos[17 $CellContext`z], Rational[300245939, 173946175488000] Cos[$CellContext`z] + Rational[-1193766593741, 1363738015825920000] Cos[3 $CellContext`z] + Rational[-10194121, 86973087744000] Cos[5 $CellContext`z] + Rational[55617547, 2435246456832000] Cos[7 $CellContext`z] + Rational[-30253, 53271016243200] Cos[9 $CellContext`z] + Rational[-28361, 1826434842624000] Cos[11 $CellContext`z] + Rational[17, 106542032486400] Cos[13 $CellContext`z] + Rational[-1, 3196260974592000] Cos[15 $CellContext`z] + Rational[1, 17579435360256000] Cos[19 $CellContext`z], Rational[64306539779, 10909904126607360000] Cos[$CellContext`z] + Rational[-1087026917, 3131031158784000] Cos[3 $CellContext`z] + Rational[767116375621, 21819808253214720000] Cos[5 $CellContext`z] + Rational[468897223, 170467251978240000] Cos[7 $CellContext`z] + Rational[-21665887, 75144747810816000] Cos[9 $CellContext`z] + Rational[7663, 1704672519782400] Cos[11 $CellContext`z] + Rational[189053, 2045607023738880000] Cos[13 $CellContext`z] + Rational[-23, 69039237051187200] Cos[15 $CellContext`z] + Rational[-1, 281270965764096000] Cos[17 $CellContext`z] + Rational[-1, 7594316075630592000] Cos[21 $CellContext`z], Rational[-78221421983189, 785513097115729920000] Cos[$CellContext`z] + Rational[-3555989290829, 99747694871838720000] Cos[3 $CellContext`z] + Rational[1595308088447, 98189137139466240000] Cos[5 $CellContext`z] + Rational[-16802983705367, 23565392913471897600000] Cos[7 $CellContext`z] + Rational[-50000417, 1363738015825920000] Cos[9 $CellContext`z] + Rational[44442089, 18410463213649920000] Cos[11 $CellContext`z] + Rational[-113461, 4418511171275980800] Cos[13 $CellContext`z] + Rational[-74069, 180013418089021440000] Cos[15 $CellContext`z] + Rational[1, 13807847410237440000] Cos[17 $CellContext`z] + Rational[1, 48603622884035788800] Cos[19 $CellContext`z] + Rational[1, 3949044359327907840000] Cos[23 $CellContext`z]}, 0, 11, 1]

Standard Form

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FractionBox[RowBox[List["Cos", "[", RowBox[List["24", " ", "z"]], "]"]], "13821655257647677440000"]]], ")"]], " ", SuperscriptBox["q", "10"]]], "+", InterpretationBox[SuperscriptBox[RowBox[List["O", "[", "q", "]"]], "11"], SeriesData[$CellContext`q, 0, List[], 0, 11, 1]]]], SeriesData[$CellContext`q, 0, List[Cos[Times[3, $CellContext`z]], Plus[Times[Rational[1, 8], Cos[$CellContext`z]], Times[Rational[-1, 16], Cos[Times[5, $CellContext`z]]]], Plus[Times[Rational[1, 64], Cos[$CellContext`z]], Times[Rational[-5, 512], Cos[Times[3, $CellContext`z]]], Times[Rational[1, 640], Cos[Times[7, $CellContext`z]]]], Plus[Times[Rational[-1, 4096], Cos[$CellContext`z]], Times[Rational[-1, 512], Cos[Times[3, $CellContext`z]]], Times[Rational[11, 40960], Cos[Times[5, $CellContext`z]]], Times[Rational[-1, 46080], Cos[Times[9, $CellContext`z]]]], Plus[Times[Rational[-21, 32768], Cos[$CellContext`z]], Times[Rational[-1621, 13107200], Cos[Times[3, $CellContext`z]]], Times[Rational[1, 16384], Cos[Times[5, 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Plus[Times[Rational[31826419, 4348654387200], Cos[$CellContext`z]], Times[Rational[70123, 33554432000], Cos[Times[3, $CellContext`z]]], Times[Rational[-326021051, 304405807104000], Cos[Times[5, $CellContext`z]]], Times[Rational[1319, 27179089920], Cos[Times[7, $CellContext`z]]], Times[Rational[7831, 4227858432000], Cos[Times[9, $CellContext`z]]], Times[Rational[-37, 832359628800], Cos[Times[11, $CellContext`z]]], Times[Rational[1, 2283043553280], Cos[Times[13, $CellContext`z]]], Times[Rational[-1, 49941577728000], Cos[Times[17, $CellContext`z]]]], Plus[Times[Rational[300245939, 173946175488000], Cos[$CellContext`z]], Times[Rational[-1193766593741, 1363738015825920000], Cos[Times[3, $CellContext`z]]], Times[Rational[-10194121, 86973087744000], Cos[Times[5, $CellContext`z]]], Times[Rational[55617547, 2435246456832000], Cos[Times[7, $CellContext`z]]], Times[Rational[-30253, 53271016243200], Cos[Times[9, $CellContext`z]]], Times[Rational[-28361, 1826434842624000], Cos[Times[11, $CellContext`z]]], Times[Rational[17, 106542032486400], Cos[Times[13, $CellContext`z]]], Times[Rational[-1, 3196260974592000], Cos[Times[15, $CellContext`z]]], Times[Rational[1, 17579435360256000], Cos[Times[19, $CellContext`z]]]], Plus[Times[Rational[64306539779, 10909904126607360000], Cos[$CellContext`z]], Times[Rational[-1087026917, 3131031158784000], Cos[Times[3, $CellContext`z]]], Times[Rational[767116375621, 21819808253214720000], Cos[Times[5, $CellContext`z]]], Times[Rational[468897223, 170467251978240000], Cos[Times[7, $CellContext`z]]], Times[Rational[-21665887, 75144747810816000], Cos[Times[9, $CellContext`z]]], Times[Rational[7663, 1704672519782400], Cos[Times[11, $CellContext`z]]], Times[Rational[189053, 2045607023738880000], Cos[Times[13, $CellContext`z]]], Times[Rational[-23, 69039237051187200], Cos[Times[15, $CellContext`z]]], Times[Rational[-1, 281270965764096000], Cos[Times[17, $CellContext`z]]], Times[Rational[-1, 7594316075630592000], Cos[Times[21, $CellContext`z]]]], Plus[Times[Rational[-78221421983189, 785513097115729920000], Cos[$CellContext`z]], Times[Rational[-3555989290829, 99747694871838720000], Cos[Times[3, $CellContext`z]]], Times[Rational[1595308088447, 98189137139466240000], Cos[Times[5, $CellContext`z]]], Times[Rational[-16802983705367, 23565392913471897600000], Cos[Times[7, $CellContext`z]]], Times[Rational[-50000417, 1363738015825920000], Cos[Times[9, $CellContext`z]]], Times[Rational[44442089, 18410463213649920000], Cos[Times[11, $CellContext`z]]], Times[Rational[-113461, 4418511171275980800], Cos[Times[13, $CellContext`z]]], Times[Rational[-74069, 180013418089021440000], Cos[Times[15, $CellContext`z]]], Times[Rational[1, 13807847410237440000], Cos[Times[17, $CellContext`z]]], Times[Rational[1, 48603622884035788800], Cos[Times[19, $CellContext`z]]], Times[Rational[1, 3949044359327907840000], Cos[Times[23, $CellContext`z]]]]], 0, 11, 1]]]]]]

MathML Form

<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mi> Ce </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <msub> <semantics> <mi> a </mi> <annotation-xml encoding='MathML-Content'> <ci> MathieuCharacteristicA </ci> </annotation-xml> </semantics> <mn> 4 </mn> </msub> <mo> ( </mo> <mi> q </mi> <mo> ) </mo> </mrow> <mo> , </mo> <mi> q </mi> <mo> , </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> ∝ </mo> <semantics> <mrow> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mfrac> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mn> 8 </mn> </mfrac> <mo> - </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 16 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 5 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mi> q </mi> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mfrac> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mn> 64 </mn> </mfrac> <mo> - </mo> <mrow> <mfrac> <mn> 5 </mn> <mn> 512 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 640 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 7 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> q </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mfrac> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mn> 4096 </mn> </mfrac> </mrow> <mo> - </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 512 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mfrac> <mrow> <mn> 11 </mn> <mo> ⁢ </mo> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 5 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 40960 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 9 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mn> 46080 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> q </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mfrac> <mrow> <mn> 21 </mn> <mo> ⁢ </mo> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mn> 32768 </mn> </mfrac> </mrow> <mo> - </mo> <mfrac> <mrow> <mn> 1621 </mn> <mo> ⁢ </mo> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 13107200 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 5 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mn> 16384 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 11 </mn> <mo> ⁢ </mo> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 7 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 2949120 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 11 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mn> 5160960 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> q </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mfrac> <mrow> <mn> 14061 </mn> <mo> ⁢ </mo> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mn> 104857600 </mn> </mfrac> </mrow> <mo> + </mo> <mfrac> <mrow> <mn> 9 </mn> <mo> ⁢ </mo> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 131072 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 12329 </mn> <mo> ⁢ </mo> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 5 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 1887436800 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 7 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 3276800 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 9 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mn> 33030144 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 13 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mn> 825753600 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> q </mi> <mn> 5 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mfrac> <mrow> <mn> 699 </mn> <mo> ⁢ </mo> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mn> 838860800 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 13050583 </mn> <mo> ⁢ </mo> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 543581798400 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 533 </mn> <mo> ⁢ </mo> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 5 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 209715200 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 76679 </mn> <mo> ⁢ </mo> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 7 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 528482304000 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 17 </mn> <mo> ⁢ </mo> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 9 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 2123366400 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 11 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mn> 6606028800 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 15 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mn> 178362777600 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> q </mi> <mn> 6 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mfrac> <mrow> <mn> 31826419 </mn> <mo> ⁢ </mo> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mn> 4348654387200 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 70123 </mn> <mo> ⁢ </mo> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 33554432000 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 326021051 </mn> <mo> ⁢ </mo> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 5 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 304405807104000 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 1319 </mn> <mo> ⁢ </mo> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 7 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 27179089920 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 7831 </mn> <mo> ⁢ </mo> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 9 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 4227858432000 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 37 </mn> <mo> ⁢ </mo> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 11 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 832359628800 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 13 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mn> 2283043553280 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 17 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mn> 49941577728000 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> q </mi> <mn> 7 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mfrac> <mrow> <mn> 300245939 </mn> <mo> ⁢ </mo> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mn> 173946175488000 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 1193766593741 </mn> <mo> ⁢ </mo> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 1363738015825920000 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 10194121 </mn> <mo> ⁢ </mo> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 5 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 86973087744000 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 55617547 </mn> <mo> ⁢ </mo> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 7 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 2435246456832000 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 30253 </mn> <mo> ⁢ </mo> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 9 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 53271016243200 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 28361 </mn> <mo> ⁢ </mo> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 11 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 1826434842624000 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 17 </mn> <mo> ⁢ </mo> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 13 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 106542032486400 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 15 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mn> 3196260974592000 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 19 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mn> 17579435360256000 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> q </mi> <mn> 8 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mfrac> <mrow> <mn> 64306539779 </mn> <mo> ⁢ </mo> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mn> 10909904126607360000 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 1087026917 </mn> <mo> ⁢ </mo> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 3131031158784000 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 767116375621 </mn> <mo> ⁢ </mo> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 5 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 21819808253214720000 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 468897223 </mn> <mo> ⁢ </mo> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 7 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 170467251978240000 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 21665887 </mn> <mo> ⁢ </mo> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 9 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 75144747810816000 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 7663 </mn> <mo> ⁢ </mo> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 11 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 1704672519782400 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 189053 </mn> <mo> ⁢ </mo> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 13 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 2045607023738880000 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 23 </mn> <mo> ⁢ </mo> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 15 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 69039237051187200 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 17 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mn> 281270965764096000 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 21 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mn> 7594316075630592000 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> q </mi> <mn> 9 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mfrac> <mrow> <mn> 78221421983189 </mn> <mo> ⁢ </mo> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mn> 785513097115729920000 </mn> </mfrac> </mrow> <mo> - </mo> <mfrac> <mrow> <mn> 3555989290829 </mn> <mo> ⁢ </mo> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 99747694871838720000 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 1595308088447 </mn> <mo> ⁢ </mo> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 5 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 98189137139466240000 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 16802983705367 </mn> <mo> ⁢ </mo> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 7 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 23565392913471897600000 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 50000417 </mn> <mo> ⁢ </mo> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 9 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 1363738015825920000 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 44442089 </mn> <mo> ⁢ </mo> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 11 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 18410463213649920000 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 113461 </mn> <mo> ⁢ </mo> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 13 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 4418511171275980800 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 74069 </mn> <mo> ⁢ </mo> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 15 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 180013418089021440000 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 17 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mn> 13807847410237440000 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 19 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mn> 48603622884035788800 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 23 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mn> 3949044359327907840000 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> q </mi> <mn> 10 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mi> O </mi> <mo> ⁡ </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> <cos /> <apply> <times /> <cn type='integer'> 3 </cn> <ci> $CellContext`z </ci> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='rational'> 1 <sep /> 8 </cn> <apply> <cos /> <ci> $CellContext`z </ci> </apply> </apply> <apply> <times /> <cn type='rational'> -1 <sep /> 16 </cn> <apply> <cos /> <apply> <times /> <cn type='integer'> 5 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='rational'> 1 <sep /> 64 </cn> <apply> <cos /> <ci> $CellContext`z </ci> </apply> </apply> <apply> <times /> <cn type='rational'> -5 <sep /> 512 </cn> <apply> <cos /> <apply> <times /> <cn type='integer'> 3 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 640 </cn> <apply> <cos /> <apply> <times /> <cn type='integer'> 7 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='rational'> -1 <sep /> 4096 </cn> <apply> <cos /> <ci> $CellContext`z </ci> </apply> </apply> <apply> <times /> <cn type='rational'> -1 <sep /> 512 </cn> <apply> <cos /> <apply> <times /> <cn type='integer'> 3 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 11 <sep /> 40960 </cn> <apply> <cos /> <apply> <times /> <cn type='integer'> 5 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> -1 <sep /> 46080 </cn> <apply> <cos /> <apply> <times /> <cn type='integer'> 9 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='rational'> -21 <sep /> 32768 </cn> <apply> <cos /> <ci> $CellContext`z </ci> </apply> </apply> <apply> <times /> <cn type='rational'> -1621 <sep /> 13107200 </cn> <apply> <cos /> <apply> <times /> <cn type='integer'> 3 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 16384 </cn> <apply> <cos /> <apply> <times /> <cn type='integer'> 5 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> -11 <sep /> 2949120 </cn> <apply> <cos /> <apply> <times /> <cn type='integer'> 7 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 5160960 </cn> <apply> <cos /> <apply> <times /> <cn type='integer'> 11 </cn> <ci> $CellContext`z </ci> </apply> </apply> 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<apply> <times /> <cn type='rational'> 44442089 <sep /> 18410463213649920000 </cn> <apply> <cos /> <apply> <times /> <cn type='integer'> 11 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> -113461 <sep /> 4418511171275980800 </cn> <apply> <cos /> <apply> <times /> <cn type='integer'> 13 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> -74069 <sep /> 180013418089021440000 </cn> <apply> <cos /> <apply> <times /> <cn type='integer'> 15 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 13807847410237440000 </cn> <apply> <cos /> <apply> <times /> <cn type='integer'> 17 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 48603622884035788800 </cn> <apply> <cos /> <apply> <times /> <cn type='integer'> 19 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 3949044359327907840000 </cn> <apply> <cos /> <apply> <times /> <cn type='integer'> 23 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> </apply> </list> <cn type='integer'> 0 </cn> <cn type='integer'> 11 </cn> <cn type='integer'> 1 </cn> </apply> </apply> </annotation-xml> </semantics> </math>

Rule Form

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

2001-10-29