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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/11.05.06.0004.01









  


  










Input Form





MathieuCharacteristicA[2, q] \[Proportional] SeriesData[$CellContext`q, 0, {4, 0, Rational[5, 12], 0, Rational[-763, 13824], 0, Rational[1002401, 79626240], 0, Rational[-1669068401, 458647142400], 0, Rational[4363384401463, 3698530556313600], 0, Rational[-40755179450909507, 99416501353709568000], 0, Rational[170942293775248009327, 1145278095594734223360000], 0, Rational[-11586143933886768007817, 206150057207052160204800000], 0, Rational[27218491783251329740936233551, 1253920091965327187575308288000000], 0, Rational[-475590687175353210308450391084589, 55613863918846191423340073189376000000]}, 0, 21, 1]










Standard Form





Cell[BoxData[RowBox[List[RowBox[List["MathieuCharacteristicA", "[", RowBox[List["2", ",", "q"]], "]"]], "\[Proportional]", InterpretationBox[RowBox[List["4", "+", FractionBox[RowBox[List["5", " ", SuperscriptBox["q", "2"]]], "12"], "-", FractionBox[RowBox[List["763", " ", SuperscriptBox["q", "4"]]], "13824"], "+", FractionBox[RowBox[List["1002401", " ", SuperscriptBox["q", "6"]]], "79626240"], "-", FractionBox[RowBox[List["1669068401", " ", SuperscriptBox["q", "8"]]], "458647142400"], "+", FractionBox[RowBox[List["4363384401463", " ", SuperscriptBox["q", "10"]]], "3698530556313600"], "-", FractionBox[RowBox[List["40755179450909507", " ", SuperscriptBox["q", "12"]]], "99416501353709568000"], "+", FractionBox[RowBox[List["170942293775248009327", " ", SuperscriptBox["q", "14"]]], "1145278095594734223360000"], "-", FractionBox[RowBox[List["11586143933886768007817", " ", SuperscriptBox["q", "16"]]], "206150057207052160204800000"], "+", FractionBox[RowBox[List["27218491783251329740936233551", " ", SuperscriptBox["q", "18"]]], "1253920091965327187575308288000000"], "-", FractionBox[RowBox[List["475590687175353210308450391084589", " ", SuperscriptBox["q", "20"]]], "55613863918846191423340073189376000000"], "+", InterpretationBox[SuperscriptBox[RowBox[List["O", "[", "q", "]"]], "21"], SeriesData[$CellContext`q, 0, List[], 0, 21, 1]]]], SeriesData[$CellContext`q, 0, List[4, 0, Rational[5, 12], 0, Rational[-763, 13824], 0, Rational[1002401, 79626240], 0, Rational[-1669068401, 458647142400], 0, Rational[4363384401463, 3698530556313600], 0, Rational[-40755179450909507, 99416501353709568000], 0, Rational[170942293775248009327, 1145278095594734223360000], 0, Rational[-11586143933886768007817, 206150057207052160204800000], 0, Rational[27218491783251329740936233551, 1253920091965327187575308288000000], 0, Rational[-475590687175353210308450391084589, 55613863918846191423340073189376000000]], 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> 2 </mn> </msub> <mo> ( </mo> <mi> q </mi> <mo> ) </mo> </mrow> <mo> &#8733; </mo> <semantics> <mrow> <mn> 4 </mn> <mo> + </mo> <mfrac> <mrow> <mn> 5 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 2 </mn> </msup> </mrow> <mn> 12 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 763 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 4 </mn> </msup> </mrow> <mn> 13824 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 1002401 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 6 </mn> </msup> </mrow> <mn> 79626240 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 1669068401 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 8 </mn> </msup> </mrow> <mn> 458647142400 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 4363384401463 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 10 </mn> </msup> </mrow> <mn> 3698530556313600 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 40755179450909507 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 12 </mn> </msup> </mrow> <mn> 99416501353709568000 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 170942293775248009327 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 14 </mn> </msup> </mrow> <mn> 1145278095594734223360000 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 11586143933886768007817 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 16 </mn> </msup> </mrow> <mn> 206150057207052160204800000 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 27218491783251329740936233551 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 18 </mn> </msup> </mrow> <mn> 1253920091965327187575308288000000 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 475590687175353210308450391084589 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 20 </mn> </msup> </mrow> <mn> 55613863918846191423340073189376000000 </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='integer'> 4 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 5 <sep /> 12 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> -763 <sep /> 13824 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 1002401 <sep /> 79626240 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> -1669068401 <sep /> 458647142400 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 4363384401463 <sep /> 3698530556313600 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> -40755179450909507 <sep /> 99416501353709568000 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 170942293775248009327 <sep /> 1145278095594734223360000 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> -11586143933886768007817 <sep /> 206150057207052160204800000 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 27218491783251329740936233551 <sep /> 1253920091965327187575308288000000 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> -475590687175353210308450391084589 <sep /> 55613863918846191423340073189376000000 </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'> 2 </cn> <ci> q </ci> </apply> <apply> <ci> SeriesData </ci> <ci> $CellContext`q </ci> <cn type='integer'> 0 </cn> <list> <cn type='integer'> 4 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 5 <sep /> 12 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> -763 <sep /> 13824 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 1002401 <sep /> 79626240 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> -1669068401 <sep /> 458647142400 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 4363384401463 <sep /> 3698530556313600 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> -40755179450909507 <sep /> 99416501353709568000 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 170942293775248009327 <sep /> 1145278095594734223360000 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> -11586143933886768007817 <sep /> 206150057207052160204800000 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 27218491783251329740936233551 <sep /> 1253920091965327187575308288000000 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> -475590687175353210308450391084589 <sep /> 55613863918846191423340073189376000000 </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["2", ",", "q_"]], "]"]], "]"]], "\[RuleDelayed]", InterpretationBox[RowBox[List["4", "+", RowBox[List[FractionBox["5", "12"], " ", SuperscriptBox["$CellContext`q", "2"]]], "-", RowBox[List[FractionBox["763", "13824"], " ", SuperscriptBox["$CellContext`q", "4"]]], "+", RowBox[List[FractionBox["1002401", "79626240"], " ", SuperscriptBox["$CellContext`q", "6"]]], "-", RowBox[List[FractionBox["1669068401", "458647142400"], " ", SuperscriptBox["$CellContext`q", "8"]]], "+", RowBox[List[FractionBox["4363384401463", "3698530556313600"], " ", SuperscriptBox["$CellContext`q", "10"]]], "-", RowBox[List[FractionBox["40755179450909507", "99416501353709568000"], " ", SuperscriptBox["$CellContext`q", "12"]]], "+", RowBox[List[FractionBox["170942293775248009327", "1145278095594734223360000"], " ", SuperscriptBox["$CellContext`q", "14"]]], "-", RowBox[List[FractionBox["11586143933886768007817", "206150057207052160204800000"], " ", SuperscriptBox["$CellContext`q", "16"]]], "+", RowBox[List[FractionBox["27218491783251329740936233551", "1253920091965327187575308288000000"], " ", SuperscriptBox["$CellContext`q", "18"]]], "-", RowBox[List[FractionBox["475590687175353210308450391084589", "55613863918846191423340073189376000000"], " ", SuperscriptBox["$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[4, 0, Rational[5, 12], 0, Rational[-763, 13824], 0, Rational[1002401, 79626240], 0, Rational[-1669068401, 458647142400], 0, Rational[4363384401463, 3698530556313600], 0, Rational[-40755179450909507, 99416501353709568000], 0, Rational[170942293775248009327, 1145278095594734223360000], 0, Rational[-11586143933886768007817, 206150057207052160204800000], 0, Rational[27218491783251329740936233551, 1253920091965327187575308288000000], 0, Rational[-475590687175353210308450391084589, 55613863918846191423340073189376000000]], 0, 21, 1], Rule[Editable, False]]]]]]










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





2001-10-29





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