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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/11.02.06.0005.01









  


  










Input Form





MathieuS[MathieuCharacteristicB[2, q], q, z] \[Proportional] SeriesData[$CellContext`q, 0, {Sin[2 $CellContext`z], Rational[-1, 12] Sin[4 $CellContext`z], Rational[-1, 288] Sin[2 $CellContext`z] + Rational[1, 384] Sin[6 $CellContext`z], Rational[1, 1536] Sin[4 $CellContext`z] + Rational[-1, 23040] Sin[8 $CellContext`z], Rational[119, 2654208] Sin[2 $CellContext`z] + Rational[-19, 737280] Sin[6 $CellContext`z] + Rational[1, 2211840] Sin[10 $CellContext`z], Rational[-1373, 159252480] Sin[4 $CellContext`z] + Rational[1, 2073600] Sin[8 $CellContext`z] + Rational[-1, 309657600] Sin[12 $CellContext`z], Rational[-1003, 1415577600] Sin[2 $CellContext`z] + Rational[8941, 25480396800] Sin[6 $CellContext`z] + Rational[-1, 185794560] Sin[10 $CellContext`z] + Rational[1, 59454259200] Sin[14 $CellContext`z], Rational[123379, 917294284800] Sin[4 $CellContext`z] + Rational[-1591, 237817036800] Sin[8 $CellContext`z] + Rational[67, 1664719257600] Sin[12 $CellContext`z] + Rational[-1, 14982473318400] Sin[16 $CellContext`z], Rational[21365639, 1761205026816000] Sin[2 $CellContext`z] + Rational[-1128997, 205473919795200] Sin[6 $CellContext`z] + Rational[17, 224737099776] Sin[10 $CellContext`z] + Rational[-89, 410947839590400] Sin[14 $CellContext`z] + Rational[1, 4794391461888000] Sin[18 $CellContext`z], Rational[-335495173, 147941222252544000] Sin[4 $CellContext`z] + Rational[9073499, 86299046313984000] Sin[8 $CellContext`z] + Rational[-6571, 11506539508531200] Sin[12 $CellContext`z] + Rational[19, 21574761578496000] Sin[16 $CellContext`z] + Rational[-1, 1898579018907648000] Sin[20 $CellContext`z], Rational[-13475627293, 62135313346068480000] Sin[2 $CellContext`z] + Rational[3067835983, 33138833784569856000] Sin[6 $CellContext`z] + Rational[-19755653, 16569416892284928000] Sin[10 $CellContext`z] + Rational[7327, 2367059556040704000] Sin[14 $CellContext`z] + Rational[-71, 25314386918768640000] Sin[18 $CellContext`z] + Rational[1, 911317929075671040000] Sin[22 $CellContext`z]}, 0, 11, 1]










Standard Form





Cell[BoxData[RowBox[List[RowBox[List["MathieuS", "[", RowBox[List[RowBox[List["MathieuCharacteristicB", "[", RowBox[List["2", ",", "q"]], "]"]], ",", "q", ",", "z"]], "]"]], "\[Proportional]", InterpretationBox[RowBox[List[RowBox[List["Sin", "[", RowBox[List["2", " ", "z"]], "]"]], "-", RowBox[List[FractionBox["1", "12"], " ", RowBox[List["Sin", "[", RowBox[List["4", " ", "z"]], "]"]], " ", "q"]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", FractionBox["1", "288"]]], " ", RowBox[List["Sin", "[", RowBox[List["2", " ", "z"]], "]"]]]], "+", RowBox[List[FractionBox["1", "384"], " ", RowBox[List["Sin", "[", RowBox[List["6", " ", "z"]], "]"]]]]]], ")"]], " ", SuperscriptBox["q", "2"]]], "+", RowBox[List[RowBox[List["(", RowBox[List[FractionBox[RowBox[List["Sin", "[", RowBox[List["4", " ", "z"]], "]"]], "1536"], "-", FractionBox[RowBox[List["Sin", "[", RowBox[List["8", " ", "z"]], "]"]], "23040"]]], ")"]], " ", SuperscriptBox["q", "3"]]], "+", RowBox[List[RowBox[List["(", RowBox[List[FractionBox[RowBox[List["119", " ", RowBox[List["Sin", "[", RowBox[List["2", " ", "z"]], "]"]]]], "2654208"], "-", FractionBox[RowBox[List["19", " ", RowBox[List["Sin", "[", RowBox[List["6", " ", "z"]], "]"]]]], "737280"], "+", FractionBox[RowBox[List["Sin", "[", RowBox[List["10", " ", "z"]], "]"]], "2211840"]]], ")"]], " ", SuperscriptBox["q", "4"]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", FractionBox[RowBox[List["1373", " ", RowBox[List["Sin", "[", RowBox[List["4", " ", "z"]], "]"]]]], "159252480"]]], "+", FractionBox[RowBox[List["Sin", "[", RowBox[List["8", " ", "z"]], "]"]], "2073600"], "-", FractionBox[RowBox[List["Sin", "[", RowBox[List["12", " ", "z"]], "]"]], "309657600"]]], ")"]], " ", SuperscriptBox["q", "5"]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", FractionBox[RowBox[List["1003", " ", RowBox[List["Sin", "[", RowBox[List["2", " ", "z"]], "]"]]]], "1415577600"]]], "+", FractionBox[RowBox[List["8941", " ", RowBox[List["Sin", "[", RowBox[List["6", " ", "z"]], "]"]]]], "25480396800"], "-", FractionBox[RowBox[List["Sin", "[", RowBox[List["10", " ", "z"]], "]"]], "185794560"], "+", FractionBox[RowBox[List["Sin", "[", RowBox[List["14", " ", "z"]], "]"]], "59454259200"]]], ")"]], " ", SuperscriptBox["q", "6"]]], "+", RowBox[List[RowBox[List["(", RowBox[List[FractionBox[RowBox[List["123379", " ", RowBox[List["Sin", "[", RowBox[List["4", " ", "z"]], "]"]]]], "917294284800"], "-", FractionBox[RowBox[List["1591", " ", RowBox[List["Sin", "[", RowBox[List["8", " ", "z"]], "]"]]]], "237817036800"], "+", FractionBox[RowBox[List["67", " ", RowBox[List["Sin", "[", RowBox[List["12", " ", "z"]], "]"]]]], "1664719257600"], "-", FractionBox[RowBox[List["Sin", "[", RowBox[List["16", " ", "z"]], "]"]], "14982473318400"]]], ")"]], " ", SuperscriptBox["q", "7"]]], "+", RowBox[List[RowBox[List["(", RowBox[List[FractionBox[RowBox[List["21365639", " ", RowBox[List["Sin", "[", RowBox[List["2", " ", "z"]], "]"]]]], "1761205026816000"], "-", FractionBox[RowBox[List["1128997", " ", RowBox[List["Sin", "[", RowBox[List["6", " ", "z"]], "]"]]]], "205473919795200"], "+", FractionBox[RowBox[List["17", " ", RowBox[List["Sin", "[", RowBox[List["10", " ", "z"]], "]"]]]], "224737099776"], "-", FractionBox[RowBox[List["89", " ", RowBox[List["Sin", "[", RowBox[List["14", " ", "z"]], "]"]]]], "410947839590400"], "+", FractionBox[RowBox[List["Sin", "[", RowBox[List["18", " ", "z"]], "]"]], "4794391461888000"]]], ")"]], " ", SuperscriptBox["q", "8"]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", FractionBox[RowBox[List["335495173", " ", RowBox[List["Sin", "[", RowBox[List["4", " ", "z"]], "]"]]]], "147941222252544000"]]], "+", FractionBox[RowBox[List["9073499", " ", RowBox[List["Sin", "[", RowBox[List["8", " ", "z"]], "]"]]]], "86299046313984000"], "-", FractionBox[RowBox[List["6571", " ", RowBox[List["Sin", "[", RowBox[List["12", " ", "z"]], "]"]]]], "11506539508531200"], "+", FractionBox[RowBox[List["19", " ", RowBox[List["Sin", "[", RowBox[List["16", " ", "z"]], "]"]]]], "21574761578496000"], "-", FractionBox[RowBox[List["Sin", "[", RowBox[List["20", " ", "z"]], "]"]], "1898579018907648000"]]], ")"]], " ", SuperscriptBox["q", "9"]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", FractionBox[RowBox[List["13475627293", " ", RowBox[List["Sin", "[", RowBox[List["2", " ", "z"]], "]"]]]], "62135313346068480000"]]], "+", FractionBox[RowBox[List["3067835983", " ", RowBox[List["Sin", "[", RowBox[List["6", " ", "z"]], "]"]]]], "33138833784569856000"], "-", FractionBox[RowBox[List["19755653", " ", RowBox[List["Sin", "[", RowBox[List["10", " ", "z"]], "]"]]]], "16569416892284928000"], "+", FractionBox[RowBox[List["7327", " ", RowBox[List["Sin", "[", RowBox[List["14", " ", "z"]], "]"]]]], "2367059556040704000"], "-", FractionBox[RowBox[List["71", " ", RowBox[List["Sin", "[", RowBox[List["18", " ", "z"]], "]"]]]], "25314386918768640000"], "+", FractionBox[RowBox[List["Sin", "[", RowBox[List["22", " ", "z"]], "]"]], "911317929075671040000"]]], ")"]], " ", SuperscriptBox["q", "10"]]], "+", InterpretationBox[SuperscriptBox[RowBox[List["O", "[", "q", "]"]], "11"], SeriesData[$CellContext`q, 0, List[], 0, 11, 1]]]], SeriesData[$CellContext`q, 0, List[Sin[Times[2, $CellContext`z]], Times[Rational[-1, 12], Sin[Times[4, $CellContext`z]]], Plus[Times[Rational[-1, 288], Sin[Times[2, $CellContext`z]]], Times[Rational[1, 384], Sin[Times[6, $CellContext`z]]]], Plus[Times[Rational[1, 1536], Sin[Times[4, $CellContext`z]]], Times[Rational[-1, 23040], Sin[Times[8, $CellContext`z]]]], Plus[Times[Rational[119, 2654208], Sin[Times[2, $CellContext`z]]], Times[Rational[-19, 737280], Sin[Times[6, $CellContext`z]]], Times[Rational[1, 2211840], Sin[Times[10, $CellContext`z]]]], Plus[Times[Rational[-1373, 159252480], Sin[Times[4, $CellContext`z]]], Times[Rational[1, 2073600], Sin[Times[8, $CellContext`z]]], Times[Rational[-1, 309657600], Sin[Times[12, $CellContext`z]]]], Plus[Times[Rational[-1003, 1415577600], Sin[Times[2, $CellContext`z]]], Times[Rational[8941, 25480396800], Sin[Times[6, $CellContext`z]]], Times[Rational[-1, 185794560], Sin[Times[10, $CellContext`z]]], Times[Rational[1, 59454259200], Sin[Times[14, $CellContext`z]]]], Plus[Times[Rational[123379, 917294284800], Sin[Times[4, $CellContext`z]]], Times[Rational[-1591, 237817036800], Sin[Times[8, $CellContext`z]]], Times[Rational[67, 1664719257600], Sin[Times[12, $CellContext`z]]], Times[Rational[-1, 14982473318400], Sin[Times[16, $CellContext`z]]]], Plus[Times[Rational[21365639, 1761205026816000], Sin[Times[2, $CellContext`z]]], Times[Rational[-1128997, 205473919795200], Sin[Times[6, $CellContext`z]]], Times[Rational[17, 224737099776], Sin[Times[10, $CellContext`z]]], Times[Rational[-89, 410947839590400], Sin[Times[14, $CellContext`z]]], Times[Rational[1, 4794391461888000], Sin[Times[18, $CellContext`z]]]], Plus[Times[Rational[-335495173, 147941222252544000], Sin[Times[4, $CellContext`z]]], Times[Rational[9073499, 86299046313984000], Sin[Times[8, $CellContext`z]]], Times[Rational[-6571, 11506539508531200], Sin[Times[12, $CellContext`z]]], Times[Rational[19, 21574761578496000], Sin[Times[16, $CellContext`z]]], Times[Rational[-1, 1898579018907648000], Sin[Times[20, $CellContext`z]]]], Plus[Times[Rational[-13475627293, 62135313346068480000], Sin[Times[2, $CellContext`z]]], Times[Rational[3067835983, 33138833784569856000], Sin[Times[6, $CellContext`z]]], Times[Rational[-19755653, 16569416892284928000], Sin[Times[10, $CellContext`z]]], Times[Rational[7327, 2367059556040704000], Sin[Times[14, $CellContext`z]]], Times[Rational[-71, 25314386918768640000], Sin[Times[18, $CellContext`z]]], Times[Rational[1, 911317929075671040000], Sin[Times[22, $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> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <msub> <semantics> <mi> b </mi> <annotation-xml encoding='MathML-Content'> <ci> MathieuCharacteristicB </ci> </annotation-xml> </semantics> <mn> 2 </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> &#8733; </mo> <semantics> <mrow> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 12 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> q </mi> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mfrac> <mn> 1 </mn> <mn> 384 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 6 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 288 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mfrac> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mn> 1536 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 8 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mn> 23040 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mfrac> <mrow> <mn> 119 </mn> <mo> &#8290; </mo> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 2654208 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 19 </mn> <mo> &#8290; </mo> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 6 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 737280 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 10 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mn> 2211840 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mfrac> <mrow> <mn> 1373 </mn> <mo> &#8290; </mo> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 159252480 </mn> </mfrac> </mrow> <mo> + </mo> <mfrac> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 8 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mn> 2073600 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 12 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mn> 309657600 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 5 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mfrac> <mrow> <mn> 1003 </mn> <mo> &#8290; </mo> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 1415577600 </mn> </mfrac> </mrow> <mo> + </mo> <mfrac> <mrow> <mn> 8941 </mn> <mo> &#8290; </mo> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 6 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 25480396800 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 10 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mn> 185794560 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 14 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mn> 59454259200 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 6 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mfrac> <mrow> <mn> 123379 </mn> <mo> &#8290; </mo> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 917294284800 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 1591 </mn> <mo> &#8290; </mo> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 8 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 237817036800 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 67 </mn> <mo> &#8290; </mo> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 12 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 1664719257600 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 16 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mn> 14982473318400 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 7 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mfrac> <mrow> <mn> 21365639 </mn> <mo> &#8290; </mo> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 1761205026816000 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 1128997 </mn> <mo> &#8290; </mo> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 6 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 205473919795200 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 17 </mn> <mo> &#8290; </mo> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 10 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 224737099776 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 89 </mn> <mo> &#8290; </mo> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 14 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 410947839590400 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 18 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mn> 4794391461888000 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 8 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mfrac> <mrow> <mn> 335495173 </mn> <mo> &#8290; </mo> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 147941222252544000 </mn> </mfrac> </mrow> <mo> + </mo> <mfrac> <mrow> <mn> 9073499 </mn> <mo> &#8290; </mo> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 8 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 86299046313984000 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 6571 </mn> <mo> &#8290; </mo> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 12 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 11506539508531200 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 19 </mn> <mo> &#8290; </mo> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 16 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 21574761578496000 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 20 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mn> 1898579018907648000 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 9 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mfrac> <mrow> <mn> 13475627293 </mn> <mo> &#8290; </mo> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 62135313346068480000 </mn> </mfrac> </mrow> <mo> + </mo> <mfrac> <mrow> <mn> 3067835983 </mn> <mo> &#8290; </mo> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 6 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 33138833784569856000 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 19755653 </mn> <mo> &#8290; </mo> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 10 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 16569416892284928000 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 7327 </mn> <mo> &#8290; </mo> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 14 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 2367059556040704000 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 71 </mn> <mo> &#8290; </mo> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 18 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 25314386918768640000 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 22 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mn> 911317929075671040000 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 10 </mn> </msup> </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> <sin /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> $CellContext`z </ci> </apply> </apply> <apply> <times /> <cn type='rational'> -1 <sep /> 12 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 4 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='rational'> -1 <sep /> 288 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 384 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 6 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='rational'> 1 <sep /> 1536 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 4 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> -1 <sep /> 23040 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 8 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='rational'> 119 <sep /> 2654208 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> -19 <sep /> 737280 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 6 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 2211840 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 10 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='rational'> -1373 <sep /> 159252480 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 4 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 2073600 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 8 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> -1 <sep /> 309657600 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 12 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='rational'> -1003 <sep /> 1415577600 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 8941 <sep /> 25480396800 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 6 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> -1 <sep /> 185794560 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 10 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 59454259200 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 14 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='rational'> 123379 <sep /> 917294284800 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 4 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> -1591 <sep /> 237817036800 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 8 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 67 <sep /> 1664719257600 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 12 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> -1 <sep /> 14982473318400 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 16 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='rational'> 21365639 <sep /> 1761205026816000 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> -1128997 <sep /> 205473919795200 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 6 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 17 <sep /> 224737099776 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 10 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> -89 <sep /> 410947839590400 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 14 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 4794391461888000 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 18 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='rational'> -335495173 <sep /> 147941222252544000 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 4 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 9073499 <sep /> 86299046313984000 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 8 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> -6571 <sep /> 11506539508531200 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 12 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 19 <sep /> 21574761578496000 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 16 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> -1 <sep /> 1898579018907648000 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 20 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='rational'> -13475627293 <sep /> 62135313346068480000 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 3067835983 <sep /> 33138833784569856000 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 6 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> -19755653 <sep /> 16569416892284928000 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 10 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 7327 <sep /> 2367059556040704000 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 14 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> -71 <sep /> 25314386918768640000 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 18 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 911317929075671040000 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 22 </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> </annotation-xml> </semantics> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Proportional </ci> <apply> <ci> Se </ci> <apply> <ci> MathieuCharacteristicB </ci> <cn type='integer'> 2 </cn> <ci> q </ci> </apply> <ci> q </ci> <ci> z </ci> </apply> <apply> <ci> SeriesData </ci> <ci> $CellContext`q </ci> <cn type='integer'> 0 </cn> <list> <apply> <sin /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> $CellContext`z </ci> </apply> </apply> <apply> <times /> <cn type='rational'> -1 <sep /> 12 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 4 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='rational'> -1 <sep /> 288 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 384 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 6 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='rational'> 1 <sep /> 1536 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 4 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> -1 <sep /> 23040 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 8 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='rational'> 119 <sep /> 2654208 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> -19 <sep /> 737280 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 6 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 2211840 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 10 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='rational'> -1373 <sep /> 159252480 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 4 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 2073600 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 8 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> -1 <sep /> 309657600 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 12 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='rational'> -1003 <sep /> 1415577600 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 8941 <sep /> 25480396800 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 6 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> -1 <sep /> 185794560 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 10 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 59454259200 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 14 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='rational'> 123379 <sep /> 917294284800 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 4 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> -1591 <sep /> 237817036800 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 8 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 67 <sep /> 1664719257600 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 12 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> -1 <sep /> 14982473318400 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 16 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='rational'> 21365639 <sep /> 1761205026816000 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> -1128997 <sep /> 205473919795200 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 6 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 17 <sep /> 224737099776 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 10 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> -89 <sep /> 410947839590400 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 14 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 4794391461888000 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 18 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='rational'> -335495173 <sep /> 147941222252544000 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 4 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 9073499 <sep /> 86299046313984000 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 8 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> -6571 <sep /> 11506539508531200 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 12 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 19 <sep /> 21574761578496000 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 16 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> -1 <sep /> 1898579018907648000 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 20 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='rational'> -13475627293 <sep /> 62135313346068480000 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 3067835983 <sep /> 33138833784569856000 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 6 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> -19755653 <sep /> 16569416892284928000 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 10 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 7327 <sep /> 2367059556040704000 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 14 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> -71 <sep /> 25314386918768640000 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 18 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 911317929075671040000 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 22 </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





© 1998- Wolfram Research, Inc.