Odd Mathieu function: Series representations (formula 11.02.06.0006)

MathieuS

$Mathematica Notation$

Mathieu and Spheroidal Functions

MathieuS[a,q,z]

Series representations

Generalized power series

Expansions at q==0

http://functions.wolfram.com/11.02.06.0006.01

Input Form

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

Standard Form

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Times[Rational[13050583, 543581798400], Sin[Times[3, $CellContext`z]]], Times[Rational[533, 209715200], Sin[Times[5, $CellContext`z]]], Times[Rational[-76679, 528482304000], Sin[Times[7, $CellContext`z]]], Times[Rational[-17, 2123366400], Sin[Times[9, $CellContext`z]]], Times[Rational[-1, 6606028800], Sin[Times[11, $CellContext`z]]], Times[Rational[1, 178362777600], Sin[Times[15, $CellContext`z]]]], Plus[Times[Rational[31826419, 4348654387200], Sin[$CellContext`z]], Times[Rational[-70123, 33554432000], Sin[Times[3, $CellContext`z]]], Times[Rational[-326021051, 304405807104000], Sin[Times[5, $CellContext`z]]], Times[Rational[-1319, 27179089920], Sin[Times[7, $CellContext`z]]], Times[Rational[7831, 4227858432000], Sin[Times[9, $CellContext`z]]], Times[Rational[37, 832359628800], Sin[Times[11, $CellContext`z]]], Times[Rational[1, 2283043553280], Sin[Times[13, $CellContext`z]]], Times[Rational[-1, 49941577728000], Sin[Times[17, $CellContext`z]]]], Plus[Times[Rational[-300245939, 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Times[Rational[-74069, 180013418089021440000], Sin[Times[15, $CellContext`z]]], Times[Rational[-1, 13807847410237440000], Sin[Times[17, $CellContext`z]]], Times[Rational[1, 48603622884035788800], Sin[Times[19, $CellContext`z]]], Times[Rational[1, 3949044359327907840000], Sin[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> Se </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <msub> <semantics> <mi> b </mi> <annotation-xml encoding='MathML-Content'> <ci> MathieuCharacteristicB </ci> </annotation-xml> </semantics> <mn> 3 </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> sin </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> sin </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> sin </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> <mrow> <mo> - </mo> <mfrac> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mn> 64 </mn> </mfrac> </mrow> <mo> - </mo> <mrow> <mfrac> <mn> 5 </mn> <mn> 512 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mi> sin </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> sin </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> sin </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> sin </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> sin </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> sin </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> <mfrac> <mrow> <mn> 21 </mn> <mo> ⁢ </mo> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mn> 32768 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 1621 </mn> <mo> ⁢ </mo> <mrow> <mi> sin </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> sin </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> sin </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> sin </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> sin </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> sin </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> sin </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> sin </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> sin </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> sin </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> <mrow> <mo> - </mo> <mfrac> <mrow> <mn> 699 </mn> <mo> ⁢ </mo> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mn> 838860800 </mn> </mfrac> </mrow> <mo> + </mo> <mfrac> <mrow> <mn> 13050583 </mn> <mo> ⁢ </mo> <mrow> <mi> sin </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> sin </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> sin </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> sin </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> sin </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> sin </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> sin </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> sin </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> sin </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> sin </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> sin </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> sin </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> sin </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> sin </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> <mrow> <mo> - </mo> <mfrac> <mrow> <mn> 300245939 </mn> <mo> ⁢ </mo> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mn> 173946175488000 </mn> </mfrac> </mrow> <mo> - </mo> <mfrac> <mrow> <mn> 1193766593741 </mn> <mo> ⁢ </mo> <mrow> <mi> sin </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> sin </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> sin </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> sin </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> sin </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> sin </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> sin </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> sin </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> sin </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> sin </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> sin </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> sin </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> sin </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> sin </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> sin </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> sin </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> sin </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> sin </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> <mfrac> <mrow> <mn> 78221421983189 </mn> <mo> ⁢ </mo> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mn> 785513097115729920000 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 3555989290829 </mn> <mo> ⁢ </mo> <mrow> <mi> sin </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> sin </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> sin </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> sin </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> sin </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> sin </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> sin </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> sin </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> sin </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> sin </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> <sin /> <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> <sin /> <ci> $CellContext`z </ci> </apply> </apply> <apply> <times /> <cn type='rational'> -1 <sep /> 16 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 5 </cn> <ci> $CellContext`z </ci> </apply> 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Rule Form

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Times[Rational[-21665887, 75144747810816000], Sin[Times[9, $CellContext`z]]], Times[Rational[-7663, 1704672519782400], Sin[Times[11, $CellContext`z]]], Times[Rational[189053, 2045607023738880000], Sin[Times[13, $CellContext`z]]], Times[Rational[23, 69039237051187200], Sin[Times[15, $CellContext`z]]], Times[Rational[-1, 281270965764096000], Sin[Times[17, $CellContext`z]]], Times[Rational[-1, 7594316075630592000], Sin[Times[21, $CellContext`z]]]], Plus[Times[Rational[78221421983189, 785513097115729920000], Sin[$CellContext`z]], Times[Rational[-3555989290829, 99747694871838720000], Sin[Times[3, $CellContext`z]]], Times[Rational[-1595308088447, 98189137139466240000], Sin[Times[5, $CellContext`z]]], Times[Rational[-16802983705367, 23565392913471897600000], Sin[Times[7, $CellContext`z]]], Times[Rational[50000417, 1363738015825920000], Sin[Times[9, $CellContext`z]]], Times[Rational[44442089, 18410463213649920000], Sin[Times[11, $CellContext`z]]], Times[Rational[113461, 4418511171275980800], Sin[Times[13, $CellContext`z]]], Times[Rational[-74069, 180013418089021440000], Sin[Times[15, $CellContext`z]]], Times[Rational[-1, 13807847410237440000], Sin[Times[17, $CellContext`z]]], Times[Rational[1, 48603622884035788800], Sin[Times[19, $CellContext`z]]], Times[Rational[1, 3949044359327907840000], Sin[Times[23, $CellContext`z]]]]], 0, 11, 1], Rule[Editable, False]]]]]]

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

2001-10-29