Wolfram Researchfunctions.wolfram.comOther Wolfram Sites
Search Site
Function CategoriesGraphics GalleryNotationsGeneral IdentitiesAbout This Site Email Comments

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/11.05.06.0010.01









  


  








Input Form





MathieuCharacteristicA[8, q] \[Proportional] SeriesData[$CellContext`q, 0, {64, 0, Rational[1, 126], 0, Rational[109, 160030080], 0, Rational[2707, 13973506525440], 0, Rational[56675690063, 22716763094823469056000], 0, Rational[-8826844303, 6088918573525228742246400], 0, Rational[96800089911697819, 343105787905984995846250718822400000], 0, Rational[1515253244196940621, 19065016210783962279192767442085478400000], 0, Rational[-718193843284873708135309579, 793447490813706069985104693586949714944720896000000], 0, Rational[2003770466274941097606322564005809, 2526377173424697820060353486656610660515990570815979520000000], 0, Rational[-279965926267161319306810784467204616783, 834262291310042453898585976646535297604118819087309409878016000000000]}, 0, 21, 1]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["MathieuCharacteristicA", "[", RowBox[List["8", ",", "q"]], "]"]], "\[Proportional]", InterpretationBox[RowBox[List["64", "+", FractionBox[SuperscriptBox["q", "2"], "126"], "+", FractionBox[RowBox[List["109", " ", SuperscriptBox["q", "4"]]], "160030080"], "+", FractionBox[RowBox[List["2707", " ", SuperscriptBox["q", "6"]]], "13973506525440"], "+", FractionBox[RowBox[List["56675690063", " ", SuperscriptBox["q", "8"]]], "22716763094823469056000"], "-", FractionBox[RowBox[List["8826844303", " ", SuperscriptBox["q", "10"]]], "6088918573525228742246400"], "+", FractionBox[RowBox[List["96800089911697819", " ", SuperscriptBox["q", "12"]]], "343105787905984995846250718822400000"], "+", FractionBox[RowBox[List["1515253244196940621", " ", SuperscriptBox["q", "14"]]], "19065016210783962279192767442085478400000"], "-", FractionBox[RowBox[List["718193843284873708135309579", " ", SuperscriptBox["q", "16"]]], "793447490813706069985104693586949714944720896000000"], "+", RowBox[List[RowBox[List["(", RowBox[List["2003770466274941097606322564005809", " ", SuperscriptBox["q", "18"]]], ")"]], "/", "2526377173424697820060353486656610660515990570815979520000000"]], "-", RowBox[List[RowBox[List["(", RowBox[List["279965926267161319306810784467204616783", " ", SuperscriptBox["q", "20"]]], ")"]], "/", "834262291310042453898585976646535297604118819087309409878016000000000"]], "+", InterpretationBox[SuperscriptBox[RowBox[List["O", "[", "q", "]"]], "21"], SeriesData[$CellContext`q, 0, List[], 0, 21, 1]]]], SeriesData[$CellContext`q, 0, List[64, 0, Rational[1, 126], 0, Rational[109, 160030080], 0, Rational[2707, 13973506525440], 0, Rational[56675690063, 22716763094823469056000], 0, Rational[-8826844303, 6088918573525228742246400], 0, Rational[96800089911697819, 343105787905984995846250718822400000], 0, Rational[1515253244196940621, 19065016210783962279192767442085478400000], 0, Rational[-718193843284873708135309579, 793447490813706069985104693586949714944720896000000], 0, Rational[2003770466274941097606322564005809, 2526377173424697820060353486656610660515990570815979520000000], 0, Rational[-279965926267161319306810784467204616783, 834262291310042453898585976646535297604118819087309409878016000000000]], 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> 8 </mn> </msub> <mo> ( </mo> <mi> q </mi> <mo> ) </mo> </mrow> <mo> &#8733; </mo> <semantics> <mrow> <mn> 64 </mn> <mo> + </mo> <mfrac> <msup> <mi> q </mi> <mn> 2 </mn> </msup> <mn> 126 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 109 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 4 </mn> </msup> </mrow> <mn> 160030080 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 2707 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 6 </mn> </msup> </mrow> <mn> 13973506525440 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 56675690063 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 8 </mn> </msup> </mrow> <mn> 22716763094823469056000 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 8826844303 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 10 </mn> </msup> </mrow> <mn> 6088918573525228742246400 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 96800089911697819 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 12 </mn> </msup> </mrow> <mn> 343105787905984995846250718822400000 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 1515253244196940621 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 14 </mn> </msup> </mrow> <mn> 19065016210783962279192767442085478400000 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 718193843284873708135309579 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 16 </mn> </msup> </mrow> <mn> 793447490813706069985104693586949714944720896000000 </mn> </mfrac> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mn> 2003770466274941097606322564005809 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 18 </mn> </msup> </mrow> <mo> ) </mo> </mrow> <mo> / </mo> <mn> 2526377173424697820060353486656610660515990570815979520000000 </mn> </mrow> <mo> - </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mn> 279965926267161319306810784467204616783 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 20 </mn> </msup> </mrow> <mo> ) </mo> </mrow> <mo> / </mo> <mn> 834262291310042453898585976646535297604118819087309409878016000000000 </mn> </mrow> <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'> 64 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 1 <sep /> 126 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 109 <sep /> 160030080 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 2707 <sep /> 13973506525440 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 56675690063 <sep /> 22716763094823469056000 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> -8826844303 <sep /> 6088918573525228742246400 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 96800089911697819 <sep /> 343105787905984995846250718822400000 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 1515253244196940621 <sep /> 19065016210783962279192767442085478400000 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> -718193843284873708135309579 <sep /> 793447490813706069985104693586949714944720896000000 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 2003770466274941097606322564005809 <sep /> 2526377173424697820060353486656610660515990570815979520000000 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> -279965926267161319306810784467204616783 <sep /> 834262291310042453898585976646535297604118819087309409878016000000000 </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'> 8 </cn> <ci> q </ci> </apply> <apply> <ci> SeriesData </ci> <ci> $CellContext`q </ci> <cn type='integer'> 0 </cn> <list> <cn type='integer'> 64 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 1 <sep /> 126 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 109 <sep /> 160030080 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 2707 <sep /> 13973506525440 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 56675690063 <sep /> 22716763094823469056000 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> -8826844303 <sep /> 6088918573525228742246400 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 96800089911697819 <sep /> 343105787905984995846250718822400000 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 1515253244196940621 <sep /> 19065016210783962279192767442085478400000 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> -718193843284873708135309579 <sep /> 793447490813706069985104693586949714944720896000000 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 2003770466274941097606322564005809 <sep /> 2526377173424697820060353486656610660515990570815979520000000 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> -279965926267161319306810784467204616783 <sep /> 834262291310042453898585976646535297604118819087309409878016000000000 </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["8", ",", "q_"]], "]"]], "]"]], "\[RuleDelayed]", InterpretationBox[RowBox[List["64", "+", RowBox[List[FractionBox["1", "126"], " ", SuperscriptBox["$CellContext`q", "2"]]], "+", RowBox[List[FractionBox["109", "160030080"], " ", SuperscriptBox["$CellContext`q", "4"]]], "+", RowBox[List[FractionBox["2707", "13973506525440"], " ", SuperscriptBox["$CellContext`q", "6"]]], "+", RowBox[List[FractionBox["56675690063", "22716763094823469056000"], " ", SuperscriptBox["$CellContext`q", "8"]]], "-", RowBox[List[FractionBox["8826844303", "6088918573525228742246400"], " ", SuperscriptBox["$CellContext`q", "10"]]], "+", RowBox[List[FractionBox["96800089911697819", "343105787905984995846250718822400000"], " ", SuperscriptBox["$CellContext`q", "12"]]], "+", RowBox[List[FractionBox["1515253244196940621", "19065016210783962279192767442085478400000"], " ", SuperscriptBox["$CellContext`q", "14"]]], "-", RowBox[List[FractionBox["718193843284873708135309579", "793447490813706069985104693586949714944720896000000"], " ", SuperscriptBox["$CellContext`q", "16"]]], "+", RowBox[List[FractionBox["2003770466274941097606322564005809", "2526377173424697820060353486656610660515990570815979520000000"], " ", SuperscriptBox["$CellContext`q", "18"]]], "-", RowBox[List[FractionBox["279965926267161319306810784467204616783", "834262291310042453898585976646535297604118819087309409878016000000000"], " ", SuperscriptBox["$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[64, 0, Rational[1, 126], 0, Rational[109, 160030080], 0, Rational[2707, 13973506525440], 0, Rational[56675690063, 22716763094823469056000], 0, Rational[-8826844303, 6088918573525228742246400], 0, Rational[96800089911697819, 343105787905984995846250718822400000], 0, Rational[1515253244196940621, 19065016210783962279192767442085478400000], 0, Rational[-718193843284873708135309579, 793447490813706069985104693586949714944720896000000], 0, Rational[2003770466274941097606322564005809, 2526377173424697820060353486656610660515990570815979520000000], 0, Rational[-279965926267161319306810784467204616783, 834262291310042453898585976646535297604118819087309409878016000000000]], 0, 21, 1], Rule[Editable, False]]]]]]


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





2001-10-29