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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/11.05.06.0002.01









  


  










Input Form





MathieuCharacteristicA[0, q] \[Proportional] SeriesData[$CellContext`q, 0, {Rational[-1, 2], 0, Rational[7, 128], 0, Rational[-29, 2304], 0, Rational[68687, 18874368], 0, Rational[-123707, 104857600], 0, Rational[8022167579, 19568944742400], 0, Rational[-286241141477, 1917756584755200], 0, Rational[7534554811777337, 134060901907751239680], 0, Rational[-63642189915976296887, 2931911924722519611801600], 0, Rational[4011632808829219892175301, 469105907955603137888256000000]}, 2, 21, 1]










Standard Form





Cell[BoxData[RowBox[List[RowBox[List["MathieuCharacteristicA", "[", RowBox[List["0", ",", "q"]], "]"]], "\[Proportional]", InterpretationBox[RowBox[List[RowBox[List["-", FractionBox[SuperscriptBox["q", "2"], "2"]]], "+", FractionBox[RowBox[List["7", " ", SuperscriptBox["q", "4"]]], "128"], "-", FractionBox[RowBox[List["29", " ", SuperscriptBox["q", "6"]]], "2304"], "+", FractionBox[RowBox[List["68687", " ", SuperscriptBox["q", "8"]]], "18874368"], "-", FractionBox[RowBox[List["123707", " ", SuperscriptBox["q", "10"]]], "104857600"], "+", FractionBox[RowBox[List["8022167579", " ", SuperscriptBox["q", "12"]]], "19568944742400"], "-", FractionBox[RowBox[List["286241141477", " ", SuperscriptBox["q", "14"]]], "1917756584755200"], "+", FractionBox[RowBox[List["7534554811777337", " ", SuperscriptBox["q", "16"]]], "134060901907751239680"], "-", FractionBox[RowBox[List["63642189915976296887", " ", SuperscriptBox["q", "18"]]], "2931911924722519611801600"], "+", FractionBox[RowBox[List["4011632808829219892175301", " ", SuperscriptBox["q", "20"]]], "469105907955603137888256000000"], "+", InterpretationBox[SuperscriptBox[RowBox[List["O", "[", "q", "]"]], "21"], SeriesData[$CellContext`q, 0, List[], 2, 21, 1]]]], SeriesData[$CellContext`q, 0, List[Rational[-1, 2], 0, Rational[7, 128], 0, Rational[-29, 2304], 0, Rational[68687, 18874368], 0, Rational[-123707, 104857600], 0, Rational[8022167579, 19568944742400], 0, Rational[-286241141477, 1917756584755200], 0, Rational[7534554811777337, 134060901907751239680], 0, Rational[-63642189915976296887, 2931911924722519611801600], 0, Rational[4011632808829219892175301, 469105907955603137888256000000]], 2, 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> 0 </mn> </msub> <mo> ( </mo> <mi> q </mi> <mo> ) </mo> </mrow> <mo> &#8733; </mo> <semantics> <mrow> <mrow> <mo> - </mo> <mfrac> <msup> <mi> q </mi> <mn> 2 </mn> </msup> <mn> 2 </mn> </mfrac> </mrow> <mo> + </mo> <mfrac> <mrow> <mn> 7 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 4 </mn> </msup> </mrow> <mn> 128 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 29 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 6 </mn> </msup> </mrow> <mn> 2304 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 68687 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 8 </mn> </msup> </mrow> <mn> 18874368 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 123707 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 10 </mn> </msup> </mrow> <mn> 104857600 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 8022167579 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 12 </mn> </msup> </mrow> <mn> 19568944742400 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 286241141477 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 14 </mn> </msup> </mrow> <mn> 1917756584755200 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 7534554811777337 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 16 </mn> </msup> </mrow> <mn> 134060901907751239680 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 63642189915976296887 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 18 </mn> </msup> </mrow> <mn> 2931911924722519611801600 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 4011632808829219892175301 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 20 </mn> </msup> </mrow> <mn> 469105907955603137888256000000 </mn> </mfrac> <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='rational'> -1 <sep /> 2 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 7 <sep /> 128 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> -29 <sep /> 2304 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 68687 <sep /> 18874368 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> -123707 <sep /> 104857600 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 8022167579 <sep /> 19568944742400 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> -286241141477 <sep /> 1917756584755200 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 7534554811777337 <sep /> 134060901907751239680 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> -63642189915976296887 <sep /> 2931911924722519611801600 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 4011632808829219892175301 <sep /> 469105907955603137888256000000 </cn> </list> <cn type='integer'> 2 </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'> 0 </cn> <ci> q </ci> </apply> <apply> <ci> SeriesData </ci> <ci> $CellContext`q </ci> <cn type='integer'> 0 </cn> <list> <cn type='rational'> -1 <sep /> 2 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 7 <sep /> 128 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> -29 <sep /> 2304 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 68687 <sep /> 18874368 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> -123707 <sep /> 104857600 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 8022167579 <sep /> 19568944742400 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> -286241141477 <sep /> 1917756584755200 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 7534554811777337 <sep /> 134060901907751239680 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> -63642189915976296887 <sep /> 2931911924722519611801600 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 4011632808829219892175301 <sep /> 469105907955603137888256000000 </cn> </list> <cn type='integer'> 2 </cn> <cn type='integer'> 21 </cn> <cn type='integer'> 1 </cn> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["MathieuCharacteristicA", "[", RowBox[List["0", ",", "q_"]], "]"]], "]"]], "\[RuleDelayed]", InterpretationBox[RowBox[List[RowBox[List["-", RowBox[List[FractionBox["1", "2"], " ", SuperscriptBox["$CellContext`q", "2"]]]]], "+", RowBox[List[FractionBox["7", "128"], " ", SuperscriptBox["$CellContext`q", "4"]]], "-", RowBox[List[FractionBox["29", "2304"], " ", SuperscriptBox["$CellContext`q", "6"]]], "+", RowBox[List[FractionBox["68687", "18874368"], " ", SuperscriptBox["$CellContext`q", "8"]]], "-", RowBox[List[FractionBox["123707", "104857600"], " ", SuperscriptBox["$CellContext`q", "10"]]], "+", RowBox[List[FractionBox["8022167579", "19568944742400"], " ", SuperscriptBox["$CellContext`q", "12"]]], "-", RowBox[List[FractionBox["286241141477", "1917756584755200"], " ", SuperscriptBox["$CellContext`q", "14"]]], "+", RowBox[List[FractionBox["7534554811777337", "134060901907751239680"], " ", SuperscriptBox["$CellContext`q", "16"]]], "-", RowBox[List[FractionBox["63642189915976296887", "2931911924722519611801600"], " ", SuperscriptBox["$CellContext`q", "18"]]], "+", RowBox[List[FractionBox["4011632808829219892175301", "469105907955603137888256000000"], " ", SuperscriptBox["$CellContext`q", "20"]]], "+", InterpretationBox[SuperscriptBox[RowBox[List["O", "[", "$CellContext`q", "]"]], "21"], SeriesData[$CellContext`q, 0, List[], 2, 21, 1], Rule[Editable, False]]]], SeriesData[$CellContext`q, 0, List[Rational[-1, 2], 0, Rational[7, 128], 0, Rational[-29, 2304], 0, Rational[68687, 18874368], 0, Rational[-123707, 104857600], 0, Rational[8022167579, 19568944742400], 0, Rational[-286241141477, 1917756584755200], 0, Rational[7534554811777337, 134060901907751239680], 0, Rational[-63642189915976296887, 2931911924722519611801600], 0, Rational[4011632808829219892175301, 469105907955603137888256000000]], 2, 21, 1], Rule[Editable, False]]]]]]










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





2001-10-29





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