Wolfram Researchfunctions.wolfram.comOther Wolfram Sites
Search Site
Function CategoriesGraphics GalleryNotationsGeneral IdentitiesAbout This Site ContributeEmail CommentsSign the Guestbook

View Related Information In
The Documentation Center
MathWorld

Download All Formulas For This Function
Mathematica Notebook
PDF File

 

Developed with Mathematica -- Download a Free Trial Version
 











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/11.05.06.0009.01









  


  










Input Form





MathieuCharacteristicA[7, q] \[Proportional] SeriesData[$CellContext`q, 0, {49, 0, Rational[1, 96], 0, Rational[7, 4423680], 0, Rational[17, 20384317440], Rational[1, 2123366400], Rational[80617, 103324028239872000], Rational[-1, 2174327193600], Rational[22381, 19044684885173207040], Rational[121, 1502894956216320000], Rational[1585697167, 475355334733923247718400000], Rational[-169, 4155203974946881536000], Rational[-4087866435403, 107331431740241997948832972800000], Rational[-619, 11770607986095528345600000], Rational[127886416305104603, 2393782869301730012493396119126016000000], Rational[-710653159, 5337927405856933273185288192000000], Rational[-4615810827596713259, 165458271926135578463543539753990225920000000], Rational[-8903677513487, 13856405477219661667865298500321280000000], Rational[6648543660666518664511, 648066959480287833726007336508428916883456000000000]}, 0, 21, 1]










Standard Form





Cell[BoxData[RowBox[List[RowBox[List["MathieuCharacteristicA", "[", RowBox[List["7", ",", "q"]], "]"]], "\[Proportional]", InterpretationBox[RowBox[List["49", "+", FractionBox[SuperscriptBox["q", "2"], "96"], "+", FractionBox[RowBox[List["7", " ", SuperscriptBox["q", "4"]]], "4423680"], "+", FractionBox[RowBox[List["17", " ", SuperscriptBox["q", "6"]]], "20384317440"], "+", FractionBox[SuperscriptBox["q", "7"], "2123366400"], "+", FractionBox[RowBox[List["80617", " ", SuperscriptBox["q", "8"]]], "103324028239872000"], "-", FractionBox[SuperscriptBox["q", "9"], "2174327193600"], "+", FractionBox[RowBox[List["22381", " ", SuperscriptBox["q", "10"]]], "19044684885173207040"], "+", FractionBox[RowBox[List["121", " ", SuperscriptBox["q", "11"]]], "1502894956216320000"], "+", FractionBox[RowBox[List["1585697167", " ", SuperscriptBox["q", "12"]]], "475355334733923247718400000"], "-", FractionBox[RowBox[List["169", " ", SuperscriptBox["q", "13"]]], "4155203974946881536000"], "-", FractionBox[RowBox[List["4087866435403", " ", SuperscriptBox["q", "14"]]], "107331431740241997948832972800000"], "-", FractionBox[RowBox[List["619", " ", SuperscriptBox["q", "15"]]], "11770607986095528345600000"], "+", FractionBox[RowBox[List["127886416305104603", " ", SuperscriptBox["q", "16"]]], "2393782869301730012493396119126016000000"], "-", FractionBox[RowBox[List["710653159", " ", SuperscriptBox["q", "17"]]], "5337927405856933273185288192000000"], "-", FractionBox[RowBox[List["4615810827596713259", " ", SuperscriptBox["q", "18"]]], "165458271926135578463543539753990225920000000"], "-", FractionBox[RowBox[List["8903677513487", " ", SuperscriptBox["q", "19"]]], "13856405477219661667865298500321280000000"], "+", FractionBox[RowBox[List["6648543660666518664511", " ", SuperscriptBox["q", "20"]]], "648066959480287833726007336508428916883456000000000"], "+", InterpretationBox[SuperscriptBox[RowBox[List["O", "[", "q", "]"]], "21"], SeriesData[$CellContext`q, 0, List[], 0, 21, 1]]]], SeriesData[$CellContext`q, 0, List[49, 0, Rational[1, 96], 0, Rational[7, 4423680], 0, Rational[17, 20384317440], Rational[1, 2123366400], Rational[80617, 103324028239872000], Rational[-1, 2174327193600], Rational[22381, 19044684885173207040], Rational[121, 1502894956216320000], Rational[1585697167, 475355334733923247718400000], Rational[-169, 4155203974946881536000], Rational[-4087866435403, 107331431740241997948832972800000], Rational[-619, 11770607986095528345600000], Rational[127886416305104603, 2393782869301730012493396119126016000000], Rational[-710653159, 5337927405856933273185288192000000], Rational[-4615810827596713259, 165458271926135578463543539753990225920000000], Rational[-8903677513487, 13856405477219661667865298500321280000000], Rational[6648543660666518664511, 648066959480287833726007336508428916883456000000000]], 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> a </mi> <annotation-xml encoding='MathML-Content'> <ci> MathieuCharacteristicA </ci> </annotation-xml> </semantics> <mn> 7 </mn> </msub> <mo> ( </mo> <mi> q </mi> <mo> ) </mo> </mrow> <mo> &#8733; </mo> <semantics> <mrow> <mn> 49 </mn> <mo> + </mo> <mfrac> <msup> <mi> q </mi> <mn> 2 </mn> </msup> <mn> 96 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 7 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 4 </mn> </msup> </mrow> <mn> 4423680 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 17 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 6 </mn> </msup> </mrow> <mn> 20384317440 </mn> </mfrac> <mo> + </mo> <mfrac> <msup> <mi> q </mi> <mn> 7 </mn> </msup> <mn> 2123366400 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 80617 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 8 </mn> </msup> </mrow> <mn> 103324028239872000 </mn> </mfrac> <mo> - </mo> <mfrac> <msup> <mi> q </mi> <mn> 9 </mn> </msup> <mn> 2174327193600 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 22381 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 10 </mn> </msup> </mrow> <mn> 19044684885173207040 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 121 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 11 </mn> </msup> </mrow> <mn> 1502894956216320000 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 1585697167 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 12 </mn> </msup> </mrow> <mn> 475355334733923247718400000 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 169 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 13 </mn> </msup> </mrow> <mn> 4155203974946881536000 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 4087866435403 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 14 </mn> </msup> </mrow> <mn> 107331431740241997948832972800000 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 619 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 15 </mn> </msup> </mrow> <mn> 11770607986095528345600000 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 127886416305104603 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 16 </mn> </msup> </mrow> <mn> 2393782869301730012493396119126016000000 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 710653159 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 17 </mn> </msup> </mrow> <mn> 5337927405856933273185288192000000 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 4615810827596713259 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 18 </mn> </msup> </mrow> <mn> 165458271926135578463543539753990225920000000 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 8903677513487 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 19 </mn> </msup> </mrow> <mn> 13856405477219661667865298500321280000000 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 6648543660666518664511 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 20 </mn> </msup> </mrow> <mn> 648066959480287833726007336508428916883456000000000 </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'> 49 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 1 <sep /> 96 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 7 <sep /> 4423680 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 17 <sep /> 20384317440 </cn> <cn type='rational'> 1 <sep /> 2123366400 </cn> <cn type='rational'> 80617 <sep /> 103324028239872000 </cn> <cn type='rational'> -1 <sep /> 2174327193600 </cn> <cn type='rational'> 22381 <sep /> 19044684885173207040 </cn> <cn type='rational'> 121 <sep /> 1502894956216320000 </cn> <cn type='rational'> 1585697167 <sep /> 475355334733923247718400000 </cn> <cn type='rational'> -169 <sep /> 4155203974946881536000 </cn> <cn type='rational'> -4087866435403 <sep /> 107331431740241997948832972800000 </cn> <cn type='rational'> -619 <sep /> 11770607986095528345600000 </cn> <cn type='rational'> 127886416305104603 <sep /> 2393782869301730012493396119126016000000 </cn> <cn type='rational'> -710653159 <sep /> 5337927405856933273185288192000000 </cn> <cn type='rational'> -4615810827596713259 <sep /> 165458271926135578463543539753990225920000000 </cn> <cn type='rational'> -8903677513487 <sep /> 13856405477219661667865298500321280000000 </cn> <cn type='rational'> 6648543660666518664511 <sep /> 648066959480287833726007336508428916883456000000000 </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'> 7 </cn> <ci> q </ci> </apply> <apply> <ci> SeriesData </ci> <ci> $CellContext`q </ci> <cn type='integer'> 0 </cn> <list> <cn type='integer'> 49 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 1 <sep /> 96 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 7 <sep /> 4423680 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 17 <sep /> 20384317440 </cn> <cn type='rational'> 1 <sep /> 2123366400 </cn> <cn type='rational'> 80617 <sep /> 103324028239872000 </cn> <cn type='rational'> -1 <sep /> 2174327193600 </cn> <cn type='rational'> 22381 <sep /> 19044684885173207040 </cn> <cn type='rational'> 121 <sep /> 1502894956216320000 </cn> <cn type='rational'> 1585697167 <sep /> 475355334733923247718400000 </cn> <cn type='rational'> -169 <sep /> 4155203974946881536000 </cn> <cn type='rational'> -4087866435403 <sep /> 107331431740241997948832972800000 </cn> <cn type='rational'> -619 <sep /> 11770607986095528345600000 </cn> <cn type='rational'> 127886416305104603 <sep /> 2393782869301730012493396119126016000000 </cn> <cn type='rational'> -710653159 <sep /> 5337927405856933273185288192000000 </cn> <cn type='rational'> -4615810827596713259 <sep /> 165458271926135578463543539753990225920000000 </cn> <cn type='rational'> -8903677513487 <sep /> 13856405477219661667865298500321280000000 </cn> <cn type='rational'> 6648543660666518664511 <sep /> 648066959480287833726007336508428916883456000000000 </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["7", ",", "q_"]], "]"]], "]"]], "\[RuleDelayed]", InterpretationBox[RowBox[List["49", "+", RowBox[List[FractionBox["1", "96"], " ", SuperscriptBox["$CellContext`q", "2"]]], "+", RowBox[List[FractionBox["7", "4423680"], " ", SuperscriptBox["$CellContext`q", "4"]]], "+", RowBox[List[FractionBox["17", "20384317440"], " ", SuperscriptBox["$CellContext`q", "6"]]], "+", RowBox[List[FractionBox["1", "2123366400"], " ", SuperscriptBox["$CellContext`q", "7"]]], "+", RowBox[List[FractionBox["80617", "103324028239872000"], " ", SuperscriptBox["$CellContext`q", "8"]]], "-", RowBox[List[FractionBox["1", "2174327193600"], " ", SuperscriptBox["$CellContext`q", "9"]]], "+", RowBox[List[FractionBox["22381", "19044684885173207040"], " ", SuperscriptBox["$CellContext`q", "10"]]], "+", RowBox[List[FractionBox["121", "1502894956216320000"], " ", SuperscriptBox["$CellContext`q", "11"]]], "+", RowBox[List[FractionBox["1585697167", "475355334733923247718400000"], " ", SuperscriptBox["$CellContext`q", "12"]]], "-", RowBox[List[FractionBox["169", "4155203974946881536000"], " ", SuperscriptBox["$CellContext`q", "13"]]], "-", RowBox[List[FractionBox["4087866435403", "107331431740241997948832972800000"], " ", SuperscriptBox["$CellContext`q", "14"]]], "-", RowBox[List[FractionBox["619", "11770607986095528345600000"], " ", SuperscriptBox["$CellContext`q", "15"]]], "+", RowBox[List[FractionBox["127886416305104603", "2393782869301730012493396119126016000000"], " ", SuperscriptBox["$CellContext`q", "16"]]], "-", RowBox[List[FractionBox["710653159", "5337927405856933273185288192000000"], " ", SuperscriptBox["$CellContext`q", "17"]]], "-", RowBox[List[FractionBox["4615810827596713259", "165458271926135578463543539753990225920000000"], " ", SuperscriptBox["$CellContext`q", "18"]]], "-", RowBox[List[FractionBox["8903677513487", "13856405477219661667865298500321280000000"], " ", SuperscriptBox["$CellContext`q", "19"]]], "+", RowBox[List[FractionBox["6648543660666518664511", "648066959480287833726007336508428916883456000000000"], " ", 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[49, 0, Rational[1, 96], 0, Rational[7, 4423680], 0, Rational[17, 20384317440], Rational[1, 2123366400], Rational[80617, 103324028239872000], Rational[-1, 2174327193600], Rational[22381, 19044684885173207040], Rational[121, 1502894956216320000], Rational[1585697167, 475355334733923247718400000], Rational[-169, 4155203974946881536000], Rational[-4087866435403, 107331431740241997948832972800000], Rational[-619, 11770607986095528345600000], Rational[127886416305104603, 2393782869301730012493396119126016000000], Rational[-710653159, 5337927405856933273185288192000000], Rational[-4615810827596713259, 165458271926135578463543539753990225920000000], Rational[-8903677513487, 13856405477219661667865298500321280000000], Rational[6648543660666518664511, 648066959480287833726007336508428916883456000000000]], 0, 21, 1], Rule[Editable, False]]]]]]










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





2001-10-29





© 1998-2014 Wolfram Research, Inc.