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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/11.05.06.0008.01









  


  








Input Form





MathieuCharacteristicA[6, q] \[Proportional] SeriesData[$CellContext`q, 0, {36, 0, Rational[1, 70], 0, Rational[187, 43904000], 0, Rational[6743617, 92935987200000], 0, Rational[-2337184771, 23315780468736000000], 0, Rational[107856094183, 1595835640971264000000000], 0, Rational[-6219042272496549577, 6566958136066696858828800000000000], 0, Rational[176848789897619589410449, 93702612251908484139256381440000000000000], 0, Rational[-1312104713817372060914843821, 430982041632244675849038417887232000000000000000], 0, Rational[159171985780417056808424886521009, 7389652564389797791681680636167910850560000000000000000], 0, Rational[-352531861885330332479936898959174099749, 6627749826390952080168132635856454570223861760000000000000000000]}, 0, 21, 1]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["MathieuCharacteristicA", "[", RowBox[List["6", ",", "q"]], "]"]], "\[Proportional]", InterpretationBox[RowBox[List["36", "+", FractionBox[SuperscriptBox["q", "2"], "70"], "+", FractionBox[RowBox[List["187", " ", SuperscriptBox["q", "4"]]], "43904000"], "+", FractionBox[RowBox[List["6743617", " ", SuperscriptBox["q", "6"]]], "92935987200000"], "-", FractionBox[RowBox[List["2337184771", " ", SuperscriptBox["q", "8"]]], "23315780468736000000"], "+", FractionBox[RowBox[List["107856094183", " ", SuperscriptBox["q", "10"]]], "1595835640971264000000000"], "-", FractionBox[RowBox[List["6219042272496549577", " ", SuperscriptBox["q", "12"]]], "6566958136066696858828800000000000"], "+", FractionBox[RowBox[List["176848789897619589410449", " ", SuperscriptBox["q", "14"]]], "93702612251908484139256381440000000000000"], "-", FractionBox[RowBox[List["1312104713817372060914843821", " ", SuperscriptBox["q", "16"]]], "430982041632244675849038417887232000000000000000"], "+", RowBox[List[RowBox[List["(", RowBox[List["159171985780417056808424886521009", " ", SuperscriptBox["q", "18"]]], ")"]], "/", "7389652564389797791681680636167910850560000000000000000"]], "-", RowBox[List[RowBox[List["(", RowBox[List["352531861885330332479936898959174099749", " ", SuperscriptBox["q", "20"]]], ")"]], "/", "6627749826390952080168132635856454570223861760000000000000000000"]], "+", InterpretationBox[SuperscriptBox[RowBox[List["O", "[", "q", "]"]], "21"], SeriesData[$CellContext`q, 0, List[], 0, 21, 1]]]], SeriesData[$CellContext`q, 0, List[36, 0, Rational[1, 70], 0, Rational[187, 43904000], 0, Rational[6743617, 92935987200000], 0, Rational[-2337184771, 23315780468736000000], 0, Rational[107856094183, 1595835640971264000000000], 0, Rational[-6219042272496549577, 6566958136066696858828800000000000], 0, Rational[176848789897619589410449, 93702612251908484139256381440000000000000], 0, Rational[-1312104713817372060914843821, 430982041632244675849038417887232000000000000000], 0, Rational[159171985780417056808424886521009, 7389652564389797791681680636167910850560000000000000000], 0, Rational[-352531861885330332479936898959174099749, 6627749826390952080168132635856454570223861760000000000000000000]], 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> 6 </mn> </msub> <mo> ( </mo> <mi> q </mi> <mo> ) </mo> </mrow> <mo> &#8733; </mo> <semantics> <mrow> <mn> 36 </mn> <mo> + </mo> <mfrac> <msup> <mi> q </mi> <mn> 2 </mn> </msup> <mn> 70 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 187 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 4 </mn> </msup> </mrow> <mn> 43904000 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 6743617 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 6 </mn> </msup> </mrow> <mn> 92935987200000 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 2337184771 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 8 </mn> </msup> </mrow> <mn> 23315780468736000000 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 107856094183 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 10 </mn> </msup> </mrow> <mn> 1595835640971264000000000 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 6219042272496549577 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 12 </mn> </msup> </mrow> <mn> 6566958136066696858828800000000000 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 176848789897619589410449 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 14 </mn> </msup> </mrow> <mn> 93702612251908484139256381440000000000000 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 1312104713817372060914843821 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 16 </mn> </msup> </mrow> <mn> 430982041632244675849038417887232000000000000000 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 159171985780417056808424886521009 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 18 </mn> </msup> </mrow> <mn> 7389652564389797791681680636167910850560000000000000000 </mn> </mfrac> <mo> - </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mn> 352531861885330332479936898959174099749 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 20 </mn> </msup> </mrow> <mo> ) </mo> </mrow> <mo> / </mo> <mn> 6627749826390952080168132635856454570223861760000000000000000000 </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'> 36 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 1 <sep /> 70 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 187 <sep /> 43904000 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 6743617 <sep /> 92935987200000 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> -2337184771 <sep /> 23315780468736000000 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 107856094183 <sep /> 1595835640971264000000000 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> -6219042272496549577 <sep /> 6566958136066696858828800000000000 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 176848789897619589410449 <sep /> 93702612251908484139256381440000000000000 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> -1312104713817372060914843821 <sep /> 430982041632244675849038417887232000000000000000 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 159171985780417056808424886521009 <sep /> 7389652564389797791681680636167910850560000000000000000 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> -352531861885330332479936898959174099749 <sep /> 6627749826390952080168132635856454570223861760000000000000000000 </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'> 6 </cn> <ci> q </ci> </apply> <apply> <ci> SeriesData </ci> <ci> $CellContext`q </ci> <cn type='integer'> 0 </cn> <list> <cn type='integer'> 36 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 1 <sep /> 70 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 187 <sep /> 43904000 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 6743617 <sep /> 92935987200000 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> -2337184771 <sep /> 23315780468736000000 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 107856094183 <sep /> 1595835640971264000000000 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> -6219042272496549577 <sep /> 6566958136066696858828800000000000 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 176848789897619589410449 <sep /> 93702612251908484139256381440000000000000 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> -1312104713817372060914843821 <sep /> 430982041632244675849038417887232000000000000000 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 159171985780417056808424886521009 <sep /> 7389652564389797791681680636167910850560000000000000000 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> -352531861885330332479936898959174099749 <sep /> 6627749826390952080168132635856454570223861760000000000000000000 </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





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["MathieuCharacteristicA", "[", RowBox[List["6", ",", "q_"]], "]"]], "]"]], "\[RuleDelayed]", InterpretationBox[RowBox[List["36", "+", RowBox[List[FractionBox["1", "70"], " ", SuperscriptBox["$CellContext`q", "2"]]], "+", RowBox[List[FractionBox["187", "43904000"], " ", SuperscriptBox["$CellContext`q", "4"]]], "+", RowBox[List[FractionBox["6743617", "92935987200000"], " ", SuperscriptBox["$CellContext`q", "6"]]], "-", RowBox[List[FractionBox["2337184771", "23315780468736000000"], " ", SuperscriptBox["$CellContext`q", "8"]]], "+", RowBox[List[FractionBox["107856094183", "1595835640971264000000000"], " ", SuperscriptBox["$CellContext`q", "10"]]], "-", RowBox[List[FractionBox["6219042272496549577", "6566958136066696858828800000000000"], " ", SuperscriptBox["$CellContext`q", "12"]]], "+", RowBox[List[FractionBox["176848789897619589410449", "93702612251908484139256381440000000000000"], " ", SuperscriptBox["$CellContext`q", "14"]]], "-", RowBox[List[FractionBox["1312104713817372060914843821", "430982041632244675849038417887232000000000000000"], " ", SuperscriptBox["$CellContext`q", "16"]]], "+", RowBox[List[FractionBox["159171985780417056808424886521009", "7389652564389797791681680636167910850560000000000000000"], " ", SuperscriptBox["$CellContext`q", "18"]]], "-", RowBox[List[FractionBox["352531861885330332479936898959174099749", "6627749826390952080168132635856454570223861760000000000000000000"], " ", SuperscriptBox["$CellContext`q", "20"]]], "+", InterpretationBox[SuperscriptBox[RowBox[List["O", "[", "$CellContext`q", "]"]], "21"], SeriesData[$CellContext`q, 0, List[], 0, 21, 1], Rule[Editable, False]]]], SeriesData[$CellContext`q, 0, List[36, 0, Rational[1, 70], 0, Rational[187, 43904000], 0, Rational[6743617, 92935987200000], 0, Rational[-2337184771, 23315780468736000000], 0, Rational[107856094183, 1595835640971264000000000], 0, Rational[-6219042272496549577, 6566958136066696858828800000000000], 0, Rational[176848789897619589410449, 93702612251908484139256381440000000000000], 0, Rational[-1312104713817372060914843821, 430982041632244675849038417887232000000000000000], 0, Rational[159171985780417056808424886521009, 7389652564389797791681680636167910850560000000000000000], 0, Rational[-352531861885330332479936898959174099749, 6627749826390952080168132635856454570223861760000000000000000000]], 0, 21, 1], Rule[Editable, False]]]]]]


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





2001-10-29