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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/11.06.06.0007.01









  


  










Input Form





MathieuCharacteristicB[6, q] \[Proportional] SeriesData[$CellContext`q, 0, {36, 0, Rational[1, 70], 0, Rational[187, 43904000], 0, Rational[-5861633, 92935987200000], 0, Rational[2825925629, 23315780468736000000], 0, Rational[45361065433, 1595835640971264000000000], 0, Rational[-5579610563247909577, 6566958136066696858828800000000000], 0, Rational[210968021365243733001199, 93702612251908484139256381440000000000000], 0, Rational[-17871705224834685935771821, 430982041632244675849038417887232000000000000000], 0, Rational[-139633570904270043589485822895441, 7389652564389797791681680636167910850560000000000000000], 0, Rational[399572262352900565424308968663357740251, 6627749826390952080168132635856454570223861760000000000000000000]}, 0, 21, 1]










Standard Form





Cell[BoxData[RowBox[List[RowBox[List["MathieuCharacteristicB", "[", 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["5861633", " ", SuperscriptBox["q", "6"]]], "92935987200000"], "+", FractionBox[RowBox[List["2825925629", " ", SuperscriptBox["q", "8"]]], "23315780468736000000"], "+", FractionBox[RowBox[List["45361065433", " ", SuperscriptBox["q", "10"]]], "1595835640971264000000000"], "-", FractionBox[RowBox[List["5579610563247909577", " ", SuperscriptBox["q", "12"]]], "6566958136066696858828800000000000"], "+", FractionBox[RowBox[List["210968021365243733001199", " ", SuperscriptBox["q", "14"]]], "93702612251908484139256381440000000000000"], "-", FractionBox[RowBox[List["17871705224834685935771821", " ", SuperscriptBox["q", "16"]]], "430982041632244675849038417887232000000000000000"], "-", FractionBox[RowBox[List["139633570904270043589485822895441", " ", SuperscriptBox["q", "18"]]], "7389652564389797791681680636167910850560000000000000000"], "+", FractionBox[RowBox[List["399572262352900565424308968663357740251", " ", 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[-5861633, 92935987200000], 0, Rational[2825925629, 23315780468736000000], 0, Rational[45361065433, 1595835640971264000000000], 0, Rational[-5579610563247909577, 6566958136066696858828800000000000], 0, Rational[210968021365243733001199, 93702612251908484139256381440000000000000], 0, Rational[-17871705224834685935771821, 430982041632244675849038417887232000000000000000], 0, Rational[-139633570904270043589485822895441, 7389652564389797791681680636167910850560000000000000000], 0, Rational[399572262352900565424308968663357740251, 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> b </mi> <annotation-xml encoding='MathML-Content'> <ci> MathieuCharacteristicB </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> 5861633 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 6 </mn> </msup> </mrow> <mn> 92935987200000 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 2825925629 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 8 </mn> </msup> </mrow> <mn> 23315780468736000000 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 45361065433 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 10 </mn> </msup> </mrow> <mn> 1595835640971264000000000 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 5579610563247909577 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 12 </mn> </msup> </mrow> <mn> 6566958136066696858828800000000000 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 210968021365243733001199 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 14 </mn> </msup> </mrow> <mn> 93702612251908484139256381440000000000000 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 17871705224834685935771821 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 16 </mn> </msup> </mrow> <mn> 430982041632244675849038417887232000000000000000 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 139633570904270043589485822895441 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 18 </mn> </msup> </mrow> <mn> 7389652564389797791681680636167910850560000000000000000 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 399572262352900565424308968663357740251 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 20 </mn> </msup> </mrow> <mn> 6627749826390952080168132635856454570223861760000000000000000000 </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'> 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'> -5861633 <sep /> 92935987200000 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 2825925629 <sep /> 23315780468736000000 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 45361065433 <sep /> 1595835640971264000000000 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> -5579610563247909577 <sep /> 6566958136066696858828800000000000 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 210968021365243733001199 <sep /> 93702612251908484139256381440000000000000 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> -17871705224834685935771821 <sep /> 430982041632244675849038417887232000000000000000 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> -139633570904270043589485822895441 <sep /> 7389652564389797791681680636167910850560000000000000000 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 399572262352900565424308968663357740251 <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> MathieuCharacteristicB </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'> -5861633 <sep /> 92935987200000 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 2825925629 <sep /> 23315780468736000000 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 45361065433 <sep /> 1595835640971264000000000 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> -5579610563247909577 <sep /> 6566958136066696858828800000000000 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 210968021365243733001199 <sep /> 93702612251908484139256381440000000000000 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> -17871705224834685935771821 <sep /> 430982041632244675849038417887232000000000000000 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> -139633570904270043589485822895441 <sep /> 7389652564389797791681680636167910850560000000000000000 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 399572262352900565424308968663357740251 <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["MathieuCharacteristicB", "[", 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["5861633", "92935987200000"], " ", SuperscriptBox["$CellContext`q", "6"]]], "+", RowBox[List[FractionBox["2825925629", "23315780468736000000"], " ", SuperscriptBox["$CellContext`q", "8"]]], "+", RowBox[List[FractionBox["45361065433", "1595835640971264000000000"], " ", SuperscriptBox["$CellContext`q", "10"]]], "-", RowBox[List[FractionBox["5579610563247909577", "6566958136066696858828800000000000"], " ", SuperscriptBox["$CellContext`q", "12"]]], "+", RowBox[List[FractionBox["210968021365243733001199", "93702612251908484139256381440000000000000"], " ", SuperscriptBox["$CellContext`q", "14"]]], "-", RowBox[List[FractionBox["17871705224834685935771821", "430982041632244675849038417887232000000000000000"], " ", SuperscriptBox["$CellContext`q", "16"]]], "-", RowBox[List[FractionBox["139633570904270043589485822895441", "7389652564389797791681680636167910850560000000000000000"], " ", SuperscriptBox["$CellContext`q", "18"]]], "+", RowBox[List[FractionBox["399572262352900565424308968663357740251", "6627749826390952080168132635856454570223861760000000000000000000"], " ", SuperscriptBox["$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[-5861633, 92935987200000], 0, Rational[2825925629, 23315780468736000000], 0, Rational[45361065433, 1595835640971264000000000], 0, Rational[-5579610563247909577, 6566958136066696858828800000000000], 0, Rational[210968021365243733001199, 93702612251908484139256381440000000000000], 0, Rational[-17871705224834685935771821, 430982041632244675849038417887232000000000000000], 0, Rational[-139633570904270043589485822895441, 7389652564389797791681680636167910850560000000000000000], 0, Rational[399572262352900565424308968663357740251, 6627749826390952080168132635856454570223861760000000000000000000]], 0, 21, 1], Rule[Editable, False]]]]]]










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





2001-10-29





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