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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/11.06.06.0004.01









  


  










Input Form





MathieuCharacteristicB[3, q] \[Proportional] SeriesData[$CellContext`q, 0, {9, 0, Rational[1, 16], Rational[-1, 64], Rational[13, 20480], Rational[5, 16384], Rational[-1961, 23592960], Rational[609, 104857600], Rational[4957199, 2113929216000], Rational[-872713, 1087163596800], Rational[421511, 6012954214400], Rational[16738435813, 681869007912960000], Rational[-572669780189, 60115798248652800000], Rational[27992567161, 29093077670952960000], Rational[110350873865291, 377046286615550361600000], Rational[-10234605999596669, 81441997908958878105600000], Rational[704720978382089561, 49548909345104858185728000000], Rational[195640795481512957, 52122878661733681987584000000], Rational[-40878632822977874980039, 23117539144052122635133255680000000], Rational[38723118606468500148773, 175807458181927253620272660480000000], Rational[96836518225571706158506019, 1923379256785136603243086872576000000000]}, 0, 21, 1]










Standard Form





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MathML Form







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</mo> <msup> <mi> q </mi> <mn> 20 </mn> </msup> </mrow> <mn> 1923379256785136603243086872576000000000 </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'> 9 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 1 <sep /> 16 </cn> <cn type='rational'> -1 <sep /> 64 </cn> <cn type='rational'> 13 <sep /> 20480 </cn> <cn type='rational'> 5 <sep /> 16384 </cn> <cn type='rational'> -1961 <sep /> 23592960 </cn> <cn type='rational'> 609 <sep /> 104857600 </cn> <cn type='rational'> 4957199 <sep /> 2113929216000 </cn> <cn type='rational'> -872713 <sep /> 1087163596800 </cn> <cn type='rational'> 421511 <sep /> 6012954214400 </cn> <cn type='rational'> 16738435813 <sep /> 681869007912960000 </cn> <cn type='rational'> -572669780189 <sep /> 60115798248652800000 </cn> <cn type='rational'> 27992567161 <sep /> 29093077670952960000 </cn> <cn type='rational'> 110350873865291 <sep /> 377046286615550361600000 </cn> <cn type='rational'> -10234605999596669 <sep /> 81441997908958878105600000 </cn> <cn type='rational'> 704720978382089561 <sep /> 49548909345104858185728000000 </cn> <cn type='rational'> 195640795481512957 <sep /> 52122878661733681987584000000 </cn> <cn type='rational'> -40878632822977874980039 <sep /> 23117539144052122635133255680000000 </cn> <cn type='rational'> 38723118606468500148773 <sep /> 175807458181927253620272660480000000 </cn> <cn type='rational'> 96836518225571706158506019 <sep /> 1923379256785136603243086872576000000000 </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'> 3 </cn> <ci> q </ci> </apply> <apply> <ci> SeriesData </ci> <ci> $CellContext`q </ci> <cn type='integer'> 0 </cn> <list> <cn type='integer'> 9 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 1 <sep /> 16 </cn> <cn type='rational'> -1 <sep /> 64 </cn> <cn type='rational'> 13 <sep /> 20480 </cn> <cn type='rational'> 5 <sep /> 16384 </cn> <cn type='rational'> -1961 <sep /> 23592960 </cn> <cn type='rational'> 609 <sep /> 104857600 </cn> <cn type='rational'> 4957199 <sep /> 2113929216000 </cn> <cn type='rational'> -872713 <sep /> 1087163596800 </cn> <cn type='rational'> 421511 <sep /> 6012954214400 </cn> <cn type='rational'> 16738435813 <sep /> 681869007912960000 </cn> <cn type='rational'> -572669780189 <sep /> 60115798248652800000 </cn> <cn type='rational'> 27992567161 <sep /> 29093077670952960000 </cn> <cn type='rational'> 110350873865291 <sep /> 377046286615550361600000 </cn> <cn type='rational'> -10234605999596669 <sep /> 81441997908958878105600000 </cn> <cn type='rational'> 704720978382089561 <sep /> 49548909345104858185728000000 </cn> <cn type='rational'> 195640795481512957 <sep /> 52122878661733681987584000000 </cn> <cn type='rational'> -40878632822977874980039 <sep /> 23117539144052122635133255680000000 </cn> <cn type='rational'> 38723118606468500148773 <sep /> 175807458181927253620272660480000000 </cn> <cn type='rational'> 96836518225571706158506019 <sep /> 1923379256785136603243086872576000000000 </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["3", ",", "q_"]], "]"]], "]"]], "\[RuleDelayed]", InterpretationBox[RowBox[List["9", "+", RowBox[List[FractionBox["1", "16"], " ", SuperscriptBox["$CellContext`q", "2"]]], "-", RowBox[List[FractionBox["1", "64"], " ", SuperscriptBox["$CellContext`q", "3"]]], "+", RowBox[List[FractionBox["13", "20480"], " ", SuperscriptBox["$CellContext`q", "4"]]], "+", RowBox[List[FractionBox["5", "16384"], " ", SuperscriptBox["$CellContext`q", "5"]]], "-", RowBox[List[FractionBox["1961", "23592960"], " ", SuperscriptBox["$CellContext`q", "6"]]], "+", RowBox[List[FractionBox["609", "104857600"], " ", SuperscriptBox["$CellContext`q", "7"]]], "+", RowBox[List[FractionBox["4957199", "2113929216000"], " ", SuperscriptBox["$CellContext`q", "8"]]], "-", RowBox[List[FractionBox["872713", "1087163596800"], " ", SuperscriptBox["$CellContext`q", "9"]]], "+", RowBox[List[FractionBox["421511", "6012954214400"], " ", SuperscriptBox["$CellContext`q", "10"]]], "+", RowBox[List[FractionBox["16738435813", "681869007912960000"], " ", SuperscriptBox["$CellContext`q", "11"]]], "-", RowBox[List[FractionBox["572669780189", "60115798248652800000"], " ", SuperscriptBox["$CellContext`q", "12"]]], "+", RowBox[List[FractionBox["27992567161", "29093077670952960000"], " ", SuperscriptBox["$CellContext`q", "13"]]], "+", RowBox[List[FractionBox["110350873865291", "377046286615550361600000"], " ", SuperscriptBox["$CellContext`q", "14"]]], "-", RowBox[List[FractionBox["10234605999596669", "81441997908958878105600000"], " ", SuperscriptBox["$CellContext`q", "15"]]], "+", RowBox[List[FractionBox["704720978382089561", "49548909345104858185728000000"], " ", SuperscriptBox["$CellContext`q", "16"]]], "+", RowBox[List[FractionBox["195640795481512957", "52122878661733681987584000000"], " ", SuperscriptBox["$CellContext`q", "17"]]], "-", RowBox[List[FractionBox["40878632822977874980039", "23117539144052122635133255680000000"], " ", SuperscriptBox["$CellContext`q", "18"]]], "+", RowBox[List[FractionBox["38723118606468500148773", "175807458181927253620272660480000000"], " ", SuperscriptBox["$CellContext`q", "19"]]], "+", RowBox[List[FractionBox["96836518225571706158506019", "1923379256785136603243086872576000000000"], " ", 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[9, 0, Rational[1, 16], Rational[-1, 64], Rational[13, 20480], Rational[5, 16384], Rational[-1961, 23592960], Rational[609, 104857600], Rational[4957199, 2113929216000], Rational[-872713, 1087163596800], Rational[421511, 6012954214400], Rational[16738435813, 681869007912960000], Rational[-572669780189, 60115798248652800000], Rational[27992567161, 29093077670952960000], Rational[110350873865291, 377046286615550361600000], Rational[-10234605999596669, 81441997908958878105600000], Rational[704720978382089561, 49548909345104858185728000000], Rational[195640795481512957, 52122878661733681987584000000], Rational[-40878632822977874980039, 23117539144052122635133255680000000], Rational[38723118606468500148773, 175807458181927253620272660480000000], Rational[96836518225571706158506019, 1923379256785136603243086872576000000000]], 0, 21, 1], Rule[Editable, False]]]]]]










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





2001-10-29





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