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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/11.06.06.0005.01









  


  










Input Form





MathieuCharacteristicB[4, q] \[Proportional] SeriesData[$CellContext`q, 0, {16, 0, Rational[1, 30], 0, Rational[-317, 864000], 0, Rational[10049, 2721600000], 0, Rational[-93824197, 2006581248000000], 0, Rational[21359366443, 31603654656000000000], 0, Rational[-2860119307587541, 271841995889049600000000000], 0, Rational[674066844771031, 3923084197232640000000000000], 0, Rational[-100817210359950705228637, 34723400260812848234496000000000000000], 0, Rational[472428361549262608073838587, 9384693388489888492337233920000000000000000], 0, Rational[-154037203587442993906456195807519, 172978668536645624690759895613440000000000000000000]}, 0, 21, 1]










Standard Form





Cell[BoxData[RowBox[List[RowBox[List["MathieuCharacteristicB", "[", RowBox[List["4", ",", "q"]], "]"]], "\[Proportional]", InterpretationBox[RowBox[List["16", "+", FractionBox[SuperscriptBox["q", "2"], "30"], "-", FractionBox[RowBox[List["317", " ", SuperscriptBox["q", "4"]]], "864000"], "+", FractionBox[RowBox[List["10049", " ", SuperscriptBox["q", "6"]]], "2721600000"], "-", FractionBox[RowBox[List["93824197", " ", SuperscriptBox["q", "8"]]], "2006581248000000"], "+", FractionBox[RowBox[List["21359366443", " ", SuperscriptBox["q", "10"]]], "31603654656000000000"], "-", FractionBox[RowBox[List["2860119307587541", " ", SuperscriptBox["q", "12"]]], "271841995889049600000000000"], "+", FractionBox[RowBox[List["674066844771031", " ", SuperscriptBox["q", "14"]]], "3923084197232640000000000000"], "-", FractionBox[RowBox[List["100817210359950705228637", " ", SuperscriptBox["q", "16"]]], "34723400260812848234496000000000000000"], "+", FractionBox[RowBox[List["472428361549262608073838587", " ", SuperscriptBox["q", "18"]]], "9384693388489888492337233920000000000000000"], "-", FractionBox[RowBox[List["154037203587442993906456195807519", " ", SuperscriptBox["q", "20"]]], "172978668536645624690759895613440000000000000000000"], "+", InterpretationBox[SuperscriptBox[RowBox[List["O", "[", "q", "]"]], "21"], SeriesData[$CellContext`q, 0, List[], 0, 21, 1]]]], SeriesData[$CellContext`q, 0, List[16, 0, Rational[1, 30], 0, Rational[-317, 864000], 0, Rational[10049, 2721600000], 0, Rational[-93824197, 2006581248000000], 0, Rational[21359366443, 31603654656000000000], 0, Rational[-2860119307587541, 271841995889049600000000000], 0, Rational[674066844771031, 3923084197232640000000000000], 0, Rational[-100817210359950705228637, 34723400260812848234496000000000000000], 0, Rational[472428361549262608073838587, 9384693388489888492337233920000000000000000], 0, Rational[-154037203587442993906456195807519, 172978668536645624690759895613440000000000000000000]], 0, 21, 1]]]]]]










MathML Form







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</mo> <msup> <mi> q </mi> <mn> 10 </mn> </msup> </mrow> <mn> 31603654656000000000 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 2860119307587541 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 12 </mn> </msup> </mrow> <mn> 271841995889049600000000000 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 674066844771031 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 14 </mn> </msup> </mrow> <mn> 3923084197232640000000000000 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 100817210359950705228637 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 16 </mn> </msup> </mrow> <mn> 34723400260812848234496000000000000000 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 472428361549262608073838587 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 18 </mn> </msup> </mrow> <mn> 9384693388489888492337233920000000000000000 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 154037203587442993906456195807519 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 20 </mn> </msup> </mrow> <mn> 172978668536645624690759895613440000000000000000000 </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'> 16 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 1 <sep /> 30 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> -317 <sep /> 864000 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 10049 <sep /> 2721600000 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> -93824197 <sep /> 2006581248000000 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 21359366443 <sep /> 31603654656000000000 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> -2860119307587541 <sep /> 271841995889049600000000000 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 674066844771031 <sep /> 3923084197232640000000000000 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> -100817210359950705228637 <sep /> 34723400260812848234496000000000000000 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 472428361549262608073838587 <sep /> 9384693388489888492337233920000000000000000 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> -154037203587442993906456195807519 <sep /> 172978668536645624690759895613440000000000000000000 </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'> 4 </cn> <ci> q </ci> </apply> <apply> <ci> SeriesData </ci> <ci> $CellContext`q </ci> <cn type='integer'> 0 </cn> <list> <cn type='integer'> 16 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 1 <sep /> 30 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> -317 <sep /> 864000 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 10049 <sep /> 2721600000 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> -93824197 <sep /> 2006581248000000 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 21359366443 <sep /> 31603654656000000000 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> -2860119307587541 <sep /> 271841995889049600000000000 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 674066844771031 <sep /> 3923084197232640000000000000 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> -100817210359950705228637 <sep /> 34723400260812848234496000000000000000 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 472428361549262608073838587 <sep /> 9384693388489888492337233920000000000000000 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> -154037203587442993906456195807519 <sep /> 172978668536645624690759895613440000000000000000000 </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["4", ",", "q_"]], "]"]], "]"]], "\[RuleDelayed]", InterpretationBox[RowBox[List["16", "+", RowBox[List[FractionBox["1", "30"], " ", SuperscriptBox["$CellContext`q", "2"]]], "-", RowBox[List[FractionBox["317", "864000"], " ", SuperscriptBox["$CellContext`q", "4"]]], "+", RowBox[List[FractionBox["10049", "2721600000"], " ", SuperscriptBox["$CellContext`q", "6"]]], "-", RowBox[List[FractionBox["93824197", "2006581248000000"], " ", SuperscriptBox["$CellContext`q", "8"]]], "+", RowBox[List[FractionBox["21359366443", "31603654656000000000"], " ", SuperscriptBox["$CellContext`q", "10"]]], "-", RowBox[List[FractionBox["2860119307587541", "271841995889049600000000000"], " ", SuperscriptBox["$CellContext`q", "12"]]], "+", RowBox[List[FractionBox["674066844771031", "3923084197232640000000000000"], " ", SuperscriptBox["$CellContext`q", "14"]]], "-", RowBox[List[FractionBox["100817210359950705228637", "34723400260812848234496000000000000000"], " ", SuperscriptBox["$CellContext`q", "16"]]], "+", RowBox[List[FractionBox["472428361549262608073838587", "9384693388489888492337233920000000000000000"], " ", SuperscriptBox["$CellContext`q", "18"]]], "-", RowBox[List[FractionBox["154037203587442993906456195807519", "172978668536645624690759895613440000000000000000000"], " ", SuperscriptBox["$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[16, 0, Rational[1, 30], 0, Rational[-317, 864000], 0, Rational[10049, 2721600000], 0, Rational[-93824197, 2006581248000000], 0, Rational[21359366443, 31603654656000000000], 0, Rational[-2860119307587541, 271841995889049600000000000], 0, Rational[674066844771031, 3923084197232640000000000000], 0, Rational[-100817210359950705228637, 34723400260812848234496000000000000000], 0, Rational[472428361549262608073838587, 9384693388489888492337233920000000000000000], 0, Rational[-154037203587442993906456195807519, 172978668536645624690759895613440000000000000000000]], 0, 21, 1], Rule[Editable, False]]]]]]










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





2001-10-29





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