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MathieuCharacteristicA






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/11.05.06.0012.01









  


  










Input Form





MathieuCharacteristicA[10, q] \[Proportional] SeriesData[$CellContext`q, 0, {100, 0, Rational[1, 198], 0, Rational[169, 993586176], 0, Rational[31943, 1772341136197632], 0, Rational[1704670559, 569203604713406176690176], 0, Rational[370335410859899, 12496432546743250420538529546240], 0, Rational[-214594017197038697689, 24728051091987796768549356462392664391680], 0, Rational[5861959225549071902627, 6849020157994773168515969871284328000745635840], 0, Rational[-8114398180685822279346163, 673635344764279156614477007813514698348562609464147968], 0, Rational[1938126664701022749795786101196163, 71231950759419817062813360338411255588508033607893280150026977280], 0, Rational[-241356573945261403675626142142516673875393, 22340619180578356065\ 04427982965659891273495159651078524001326093828096000000]}, 0, 21, 1]










Standard Form





Cell[BoxData[RowBox[List[RowBox[List["MathieuCharacteristicA", "[", RowBox[List["10", ",", "q"]], "]"]], "\[Proportional]", InterpretationBox[RowBox[List["100", "+", FractionBox[SuperscriptBox["q", "2"], "198"], "+", FractionBox[RowBox[List["169", " ", SuperscriptBox["q", "4"]]], "993586176"], "+", FractionBox[RowBox[List["31943", " ", SuperscriptBox["q", "6"]]], "1772341136197632"], "+", FractionBox[RowBox[List["1704670559", " ", SuperscriptBox["q", "8"]]], "569203604713406176690176"], "+", FractionBox[RowBox[List["370335410859899", " ", SuperscriptBox["q", "10"]]], "12496432546743250420538529546240"], "-", FractionBox[RowBox[List["214594017197038697689", " ", SuperscriptBox["q", "12"]]], "24728051091987796768549356462392664391680"], "+", FractionBox[RowBox[List["5861959225549071902627", " ", SuperscriptBox["q", "14"]]], "6849020157994773168515969871284328000745635840"], "-", RowBox[List[RowBox[List["(", RowBox[List["8114398180685822279346163", " ", SuperscriptBox["q", "16"]]], ")"]], "/", "673635344764279156614477007813514698348562609464147968"]], "+", RowBox[List[RowBox[List["(", RowBox[List["1938126664701022749795786101196163", " ", SuperscriptBox["q", "18"]]], ")"]], "/", "71231950759419817062813360338411255588508033607893280150026977280"]], "-", RowBox[List[RowBox[List["(", RowBox[List["241356573945261403675626142142516673875393", " ", SuperscriptBox["q", "20"]]], ")"]], "/", "2234061918057835606504427982965659891273495159651078524001326093828096000000"]], "+", InterpretationBox[SuperscriptBox[RowBox[List["O", "[", "q", "]"]], "21"], SeriesData[$CellContext`q, 0, List[], 0, 21, 1]]]], SeriesData[$CellContext`q, 0, List[100, 0, Rational[1, 198], 0, Rational[169, 993586176], 0, Rational[31943, 1772341136197632], 0, Rational[1704670559, 569203604713406176690176], 0, Rational[370335410859899, 12496432546743250420538529546240], 0, Rational[-214594017197038697689, 24728051091987796768549356462392664391680], 0, Rational[5861959225549071902627, 6849020157994773168515969871284328000745635840], 0, Rational[-8114398180685822279346163, 673635344764279156614477007813514698348562609464147968], 0, Rational[1938126664701022749795786101196163, 71231950759419817062813360338411255588508033607893280150026977280], 0, Rational[-241356573945261403675626142142516673875393, 2234061918057835606504427982965659891273495159651078524001326093828096000000]], 0, 21, 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> <msub> <semantics> <mi> a </mi> <annotation-xml encoding='MathML-Content'> <ci> MathieuCharacteristicA </ci> </annotation-xml> </semantics> <mn> 10 </mn> </msub> <mo> ( </mo> <mi> q </mi> <mo> ) </mo> </mrow> <mo> &#8733; </mo> <semantics> <mrow> <mn> 100 </mn> <mo> + </mo> <mfrac> <msup> <mi> q </mi> <mn> 2 </mn> </msup> <mn> 198 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 169 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 4 </mn> </msup> </mrow> <mn> 993586176 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 31943 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 6 </mn> </msup> </mrow> <mn> 1772341136197632 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 1704670559 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 8 </mn> </msup> </mrow> <mn> 569203604713406176690176 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 370335410859899 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 10 </mn> </msup> </mrow> <mn> 12496432546743250420538529546240 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 214594017197038697689 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 12 </mn> </msup> </mrow> <mn> 24728051091987796768549356462392664391680 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 5861959225549071902627 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 14 </mn> </msup> </mrow> <mn> 6849020157994773168515969871284328000745635840 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 8114398180685822279346163 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 16 </mn> </msup> </mrow> <mn> 673635344764279156614477007813514698348562609464147968 </mn> </mfrac> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mn> 1938126664701022749795786101196163 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 18 </mn> </msup> </mrow> <mo> ) </mo> </mrow> <mo> / </mo> <mn> 71231950759419817062813360338411255588508033607893280150026977280 </mn> </mrow> <mo> - </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mn> 241356573945261403675626142142516673875393 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 20 </mn> </msup> </mrow> <mo> ) </mo> </mrow> <mo> / </mo> <mn> 2234061918057835606504427982965659891273495159651078524001326093828096000000 </mn> </mrow> <mo> + </mo> <mrow> <mi> O </mi> <mo> &#8289; </mo> <mo> ( </mo> <msup> <mi> q </mi> <mn> 21 </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> <cn type='integer'> 100 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 1 <sep /> 198 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 169 <sep /> 993586176 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 31943 <sep /> 1772341136197632 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 1704670559 <sep /> 569203604713406176690176 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 370335410859899 <sep /> 12496432546743250420538529546240 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> -214594017197038697689 <sep /> 24728051091987796768549356462392664391680 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 5861959225549071902627 <sep /> 6849020157994773168515969871284328000745635840 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> -8114398180685822279346163 <sep /> 673635344764279156614477007813514698348562609464147968 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 1938126664701022749795786101196163 <sep /> 71231950759419817062813360338411255588508033607893280150026977280 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> -241356573945261403675626142142516673875393 <sep /> 2234061918057835606504427982965659891273495159651078524001326093828096000000 </cn> </list> <cn type='integer'> 0 </cn> <cn type='integer'> 21 </cn> <cn type='integer'> 1 </cn> </apply> </annotation-xml> </semantics> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Proportional </ci> <apply> <ci> MathieuCharacteristicA </ci> <cn type='integer'> 10 </cn> <ci> q </ci> </apply> <apply> <ci> SeriesData </ci> <ci> $CellContext`q </ci> <cn type='integer'> 0 </cn> <list> <cn type='integer'> 100 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 1 <sep /> 198 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 169 <sep /> 993586176 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 31943 <sep /> 1772341136197632 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 1704670559 <sep /> 569203604713406176690176 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 370335410859899 <sep /> 12496432546743250420538529546240 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> -214594017197038697689 <sep /> 24728051091987796768549356462392664391680 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 5861959225549071902627 <sep /> 6849020157994773168515969871284328000745635840 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> -8114398180685822279346163 <sep /> 673635344764279156614477007813514698348562609464147968 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 1938126664701022749795786101196163 <sep /> 71231950759419817062813360338411255588508033607893280150026977280 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> -241356573945261403675626142142516673875393 <sep /> 2234061918057835606504427982965659891273495159651078524001326093828096000000 </cn> </list> <cn type='integer'> 0 </cn> <cn type='integer'> 21 </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





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