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MathieuCharacteristicB






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/11.06.06.0003.01









  


  










Input Form





MathieuCharacteristicB[2, q] \[Proportional] SeriesData[$CellContext`q, 0, {4, 0, Rational[-1, 12], 0, Rational[5, 13824], 0, Rational[-289, 79626240], 0, Rational[21391, 458647142400], 0, Rational[-2499767, 3698530556313600], 0, Rational[1046070973, 99416501353709568000], 0, Rational[-196784996207, 1145278095594734223360000], 0, Rational[598543743703, 206150057207052160204800000], 0, Rational[-63122700730716751, 1253920091965327187575308288000000], 0, Rational[49524045775449454931, 55613863918846191423340073189376000000]}, 0, 21, 1]










Standard Form





Cell[BoxData[RowBox[List[RowBox[List["MathieuCharacteristicB", "[", RowBox[List["2", ",", "q"]], "]"]], "\[Proportional]", InterpretationBox[RowBox[List["4", "-", FractionBox[SuperscriptBox["q", "2"], "12"], "+", FractionBox[RowBox[List["5", " ", SuperscriptBox["q", "4"]]], "13824"], "-", FractionBox[RowBox[List["289", " ", SuperscriptBox["q", "6"]]], "79626240"], "+", FractionBox[RowBox[List["21391", " ", SuperscriptBox["q", "8"]]], "458647142400"], "-", FractionBox[RowBox[List["2499767", " ", SuperscriptBox["q", "10"]]], "3698530556313600"], "+", FractionBox[RowBox[List["1046070973", " ", SuperscriptBox["q", "12"]]], "99416501353709568000"], "-", FractionBox[RowBox[List["196784996207", " ", SuperscriptBox["q", "14"]]], "1145278095594734223360000"], "+", FractionBox[RowBox[List["598543743703", " ", SuperscriptBox["q", "16"]]], "206150057207052160204800000"], "-", FractionBox[RowBox[List["63122700730716751", " ", SuperscriptBox["q", "18"]]], "1253920091965327187575308288000000"], "+", FractionBox[RowBox[List["49524045775449454931", " ", SuperscriptBox["q", "20"]]], "55613863918846191423340073189376000000"], "+", InterpretationBox[SuperscriptBox[RowBox[List["O", "[", "q", "]"]], "21"], SeriesData[$CellContext`q, 0, List[], 0, 21, 1], Rule[Editable, False]]]], SeriesData[$CellContext`q, 0, List[4, 0, Rational[-1, 12], 0, Rational[5, 13824], 0, Rational[-289, 79626240], 0, Rational[21391, 458647142400], 0, Rational[-2499767, 3698530556313600], 0, Rational[1046070973, 99416501353709568000], 0, Rational[-196784996207, 1145278095594734223360000], 0, Rational[598543743703, 206150057207052160204800000], 0, Rational[-63122700730716751, 1253920091965327187575308288000000], 0, Rational[49524045775449454931, 55613863918846191423340073189376000000]], 0, 21, 1], Rule[Editable, False]]]]]]










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> 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> &#8733; </mo> <semantics> <mrow> <mn> 4 </mn> <mo> - </mo> <mfrac> <msup> <mi> q </mi> <mn> 2 </mn> </msup> <mn> 12 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 5 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 4 </mn> </msup> </mrow> <mn> 13824 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 289 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 6 </mn> </msup> </mrow> <mn> 79626240 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 21391 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 8 </mn> </msup> </mrow> <mn> 458647142400 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 2499767 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 10 </mn> </msup> </mrow> <mn> 3698530556313600 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 1046070973 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 12 </mn> </msup> </mrow> <mn> 99416501353709568000 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 196784996207 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 14 </mn> </msup> </mrow> <mn> 1145278095594734223360000 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 598543743703 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 16 </mn> </msup> </mrow> <mn> 206150057207052160204800000 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 63122700730716751 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 18 </mn> </msup> </mrow> <mn> 1253920091965327187575308288000000 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 49524045775449454931 </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'> 1 </cn> <cn type='integer'> -1 </cn> <cn type='rational'> -1 <sep /> 8 </cn> <cn type='rational'> 1 <sep /> 64 </cn> <cn type='rational'> -1 <sep /> 1536 </cn> <cn type='rational'> -11 <sep /> 36864 </cn> <cn type='rational'> 49 <sep /> 589824 </cn> <cn type='rational'> -55 <sep /> 9437184 </cn> <cn type='rational'> -83 <sep /> 35389440 </cn> <cn type='rational'> 12121 <sep /> 15099494400 </cn> <cn type='rational'> -114299 <sep /> 1630745395200 </cn> <cn type='rational'> -192151 <sep /> 7827577896960 </cn> <cn type='rational'> 83513957 <sep /> 8766887244595200 </cn> <cn type='rational'> -944750239 <sep /> 981891371394662400 </cn> <cn type='rational'> -27587714461 <sep /> 94261571653887590400 </cn> <cn type='rational'> 45487147753 <sep /> 361964435150928347136 </cn> <cn type='rational'> -11583279236477 <sep /> 814419979089588781056000 </cn> <cn type='rational'> -4401918060178787 <sep /> 1172764769889007844720640000 </cn> <cn type='rational'> 20737942737397933 <sep /> 11727647698890078447206400000 </cn> <cn type='rational'> -206649295526133419 <sep /> 938211815911206275776512000000 </cn> <cn type='rational'> -230932630430735533 <sep /> 4586813322232564014907392000000 </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> MathieuCharacteristicB </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'> 1 </cn> <cn type='integer'> -1 </cn> <cn type='rational'> -1 <sep /> 8 </cn> <cn type='rational'> 1 <sep /> 64 </cn> <cn type='rational'> -1 <sep /> 1536 </cn> <cn type='rational'> -11 <sep /> 36864 </cn> <cn type='rational'> 49 <sep /> 589824 </cn> <cn type='rational'> -55 <sep /> 9437184 </cn> <cn type='rational'> -83 <sep /> 35389440 </cn> <cn type='rational'> 12121 <sep /> 15099494400 </cn> <cn type='rational'> -114299 <sep /> 1630745395200 </cn> <cn type='rational'> -192151 <sep /> 7827577896960 </cn> <cn type='rational'> 83513957 <sep /> 8766887244595200 </cn> <cn type='rational'> -944750239 <sep /> 981891371394662400 </cn> <cn type='rational'> -27587714461 <sep /> 94261571653887590400 </cn> <cn type='rational'> 45487147753 <sep /> 361964435150928347136 </cn> <cn type='rational'> -11583279236477 <sep /> 814419979089588781056000 </cn> <cn type='rational'> -4401918060178787 <sep /> 1172764769889007844720640000 </cn> <cn type='rational'> 20737942737397933 <sep /> 11727647698890078447206400000 </cn> <cn type='rational'> -206649295526133419 <sep /> 938211815911206275776512000000 </cn> <cn type='rational'> -230932630430735533 <sep /> 4586813322232564014907392000000 </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["MathieuCharacteristicB", "[", RowBox[List["2", ",", "q_"]], "]"]], "]"]], "\[RuleDelayed]", InterpretationBox[RowBox[List["4", "-", RowBox[List[FractionBox["1", "12"], " ", SuperscriptBox["$CellContext`q", "2"]]], "+", RowBox[List[FractionBox["5", "13824"], " ", SuperscriptBox["$CellContext`q", "4"]]], "-", RowBox[List[FractionBox["289", "79626240"], " ", SuperscriptBox["$CellContext`q", "6"]]], "+", RowBox[List[FractionBox["21391", "458647142400"], " ", SuperscriptBox["$CellContext`q", "8"]]], "-", RowBox[List[FractionBox["2499767", "3698530556313600"], " ", SuperscriptBox["$CellContext`q", "10"]]], "+", RowBox[List[FractionBox["1046070973", "99416501353709568000"], " ", SuperscriptBox["$CellContext`q", "12"]]], "-", RowBox[List[FractionBox["196784996207", "1145278095594734223360000"], " ", SuperscriptBox["$CellContext`q", "14"]]], "+", RowBox[List[FractionBox["598543743703", "206150057207052160204800000"], " ", SuperscriptBox["$CellContext`q", "16"]]], "-", RowBox[List[FractionBox["63122700730716751", "1253920091965327187575308288000000"], " ", SuperscriptBox["$CellContext`q", "18"]]], "+", RowBox[List[FractionBox["49524045775449454931", "55613863918846191423340073189376000000"], " ", SuperscriptBox["$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[-1, 12], 0, Rational[5, 13824], 0, Rational[-289, 79626240], 0, Rational[21391, 458647142400], 0, Rational[-2499767, 3698530556313600], 0, Rational[1046070973, 99416501353709568000], 0, Rational[-196784996207, 1145278095594734223360000], 0, Rational[598543743703, 206150057207052160204800000], 0, Rational[-63122700730716751, 1253920091965327187575308288000000], 0, Rational[49524045775449454931, 55613863918846191423340073189376000000]], 0, 21, 1], Rule[Editable, False]]]]]]










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





2001-10-29





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