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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/11.05.06.0006.01









  


  










Input Form





MathieuCharacteristicA[4, q] \[Proportional] SeriesData[$CellContext`q, 0, {16, 0, Rational[1, 30], 0, Rational[433, 864000], 0, Rational[-5701, 2721600000], 0, Rational[-112236997, 2006581248000000], 0, Rational[8417126443, 31603654656000000000], 0, Rational[2887659548698709, 271841995889049600000000000], 0, Rational[-1362879008360033, 27461589380628480000000000000], 0, Rational[-85043641535997859212637, 34723400260812848234496000000000000000], 0, Rational[100385830833154261150792187, 9384693388489888492337233920000000000000000], 0, Rational[108310756056687781830924018371231, 172978668536645624690759895613440000000000000000000]}, 0, 21, 1]










Standard Form





Cell[BoxData[RowBox[List[RowBox[List["MathieuCharacteristicA", "[", RowBox[List["4", ",", "q"]], "]"]], "\[Proportional]", InterpretationBox[RowBox[List["16", "+", FractionBox[SuperscriptBox["q", "2"], "30"], "+", FractionBox[RowBox[List["433", " ", SuperscriptBox["q", "4"]]], "864000"], "-", FractionBox[RowBox[List["5701", " ", SuperscriptBox["q", "6"]]], "2721600000"], "-", FractionBox[RowBox[List["112236997", " ", SuperscriptBox["q", "8"]]], "2006581248000000"], "+", FractionBox[RowBox[List["8417126443", " ", SuperscriptBox["q", "10"]]], "31603654656000000000"], "+", FractionBox[RowBox[List["2887659548698709", " ", SuperscriptBox["q", "12"]]], "271841995889049600000000000"], "-", FractionBox[RowBox[List["1362879008360033", " ", SuperscriptBox["q", "14"]]], "27461589380628480000000000000"], "-", FractionBox[RowBox[List["85043641535997859212637", " ", SuperscriptBox["q", "16"]]], "34723400260812848234496000000000000000"], "+", FractionBox[RowBox[List["100385830833154261150792187", " ", SuperscriptBox["q", "18"]]], "9384693388489888492337233920000000000000000"], "+", FractionBox[RowBox[List["108310756056687781830924018371231", " ", 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[433, 864000], 0, Rational[-5701, 2721600000], 0, Rational[-112236997, 2006581248000000], 0, Rational[8417126443, 31603654656000000000], 0, Rational[2887659548698709, 271841995889049600000000000], 0, Rational[-1362879008360033, 27461589380628480000000000000], 0, Rational[-85043641535997859212637, 34723400260812848234496000000000000000], 0, Rational[100385830833154261150792187, 9384693388489888492337233920000000000000000], 0, Rational[108310756056687781830924018371231, 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> 2887659548698709 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 12 </mn> </msup> </mrow> <mn> 271841995889049600000000000 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 1362879008360033 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 14 </mn> </msup> </mrow> <mn> 27461589380628480000000000000 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 85043641535997859212637 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 16 </mn> </msup> </mrow> <mn> 34723400260812848234496000000000000000 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 100385830833154261150792187 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 18 </mn> </msup> </mrow> <mn> 9384693388489888492337233920000000000000000 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 108310756056687781830924018371231 </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'> 433 <sep /> 864000 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> -5701 <sep /> 2721600000 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> -112236997 <sep /> 2006581248000000 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 8417126443 <sep /> 31603654656000000000 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 2887659548698709 <sep /> 271841995889049600000000000 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> -1362879008360033 <sep /> 27461589380628480000000000000 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> -85043641535997859212637 <sep /> 34723400260812848234496000000000000000 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 100385830833154261150792187 <sep /> 9384693388489888492337233920000000000000000 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 108310756056687781830924018371231 <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> MathieuCharacteristicA </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'> 433 <sep /> 864000 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> -5701 <sep /> 2721600000 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> -112236997 <sep /> 2006581248000000 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 8417126443 <sep /> 31603654656000000000 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 2887659548698709 <sep /> 271841995889049600000000000 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> -1362879008360033 <sep /> 27461589380628480000000000000 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> -85043641535997859212637 <sep /> 34723400260812848234496000000000000000 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 100385830833154261150792187 <sep /> 9384693388489888492337233920000000000000000 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 108310756056687781830924018371231 <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["MathieuCharacteristicA", "[", RowBox[List["4", ",", "q_"]], "]"]], "]"]], "\[RuleDelayed]", InterpretationBox[RowBox[List["16", "+", RowBox[List[FractionBox["1", "30"], " ", SuperscriptBox["$CellContext`q", "2"]]], "+", RowBox[List[FractionBox["433", "864000"], " ", SuperscriptBox["$CellContext`q", "4"]]], "-", RowBox[List[FractionBox["5701", "2721600000"], " ", SuperscriptBox["$CellContext`q", "6"]]], "-", RowBox[List[FractionBox["112236997", "2006581248000000"], " ", SuperscriptBox["$CellContext`q", "8"]]], "+", RowBox[List[FractionBox["8417126443", "31603654656000000000"], " ", SuperscriptBox["$CellContext`q", "10"]]], "+", RowBox[List[FractionBox["2887659548698709", "271841995889049600000000000"], " ", SuperscriptBox["$CellContext`q", "12"]]], "-", RowBox[List[FractionBox["1362879008360033", "27461589380628480000000000000"], " ", SuperscriptBox["$CellContext`q", "14"]]], "-", RowBox[List[FractionBox["85043641535997859212637", "34723400260812848234496000000000000000"], " ", SuperscriptBox["$CellContext`q", "16"]]], "+", RowBox[List[FractionBox["100385830833154261150792187", "9384693388489888492337233920000000000000000"], " ", SuperscriptBox["$CellContext`q", "18"]]], "+", RowBox[List[FractionBox["108310756056687781830924018371231", "172978668536645624690759895613440000000000000000000"], " ", SuperscriptBox["$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[433, 864000], 0, Rational[-5701, 2721600000], 0, Rational[-112236997, 2006581248000000], 0, Rational[8417126443, 31603654656000000000], 0, Rational[2887659548698709, 271841995889049600000000000], 0, Rational[-1362879008360033, 27461589380628480000000000000], 0, Rational[-85043641535997859212637, 34723400260812848234496000000000000000], 0, Rational[100385830833154261150792187, 9384693388489888492337233920000000000000000], 0, Rational[108310756056687781830924018371231, 172978668536645624690759895613440000000000000000000]], 0, 21, 1], Rule[Editable, False]]]]]]










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





2001-10-29





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