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
 











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/11.06.06.0009.01









  


  










Input Form





MathieuCharacteristicB[8, q] \[Proportional] SeriesData[$CellContext`q, 0, {64, 0, Rational[1, 126], 0, Rational[109, 160030080], 0, Rational[2707, 13973506525440], 0, Rational[-52492329667, 22716763094823469056000], 0, Rational[9604120067, 6088918573525228742246400], 0, Rational[-52131336111051551, 343105787905984995846250718822400000], 0, Rational[3037944758311201111, 19065016210783962279192767442085478400000], 0, Rational[-688644321431203907962783243, 793447490813706069985104693586949714944720896000000], 0, Rational[2113914045440842540935295950474929, 2526377173424697820060353486656610660515990570815979520000000], 0, Rational[-222064082834050351792146883461654210383, 834262291310042453898585976646535297604118819087309409878016000000000]}, 0, 21, 1]










Standard Form





Cell[BoxData[RowBox[List[RowBox[List["MathieuCharacteristicB", "[", 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["52492329667", " ", SuperscriptBox["q", "8"]]], "22716763094823469056000"], "+", FractionBox[RowBox[List["9604120067", " ", SuperscriptBox["q", "10"]]], "6088918573525228742246400"], "-", FractionBox[RowBox[List["52131336111051551", " ", SuperscriptBox["q", "12"]]], "343105787905984995846250718822400000"], "+", FractionBox[RowBox[List["3037944758311201111", " ", SuperscriptBox["q", "14"]]], "19065016210783962279192767442085478400000"], "-", FractionBox[RowBox[List["688644321431203907962783243", " ", SuperscriptBox["q", "16"]]], "793447490813706069985104693586949714944720896000000"], "+", FractionBox[RowBox[List["2113914045440842540935295950474929", " ", SuperscriptBox["q", "18"]]], "2526377173424697820060353486656610660515990570815979520000000"], "-", RowBox[List[RowBox[List["(", RowBox[List["222064082834050351792146883461654210383", " ", 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[-52492329667, 22716763094823469056000], 0, Rational[9604120067, 6088918573525228742246400], 0, Rational[-52131336111051551, 343105787905984995846250718822400000], 0, Rational[3037944758311201111, 19065016210783962279192767442085478400000], 0, Rational[-688644321431203907962783243, 793447490813706069985104693586949714944720896000000], 0, Rational[2113914045440842540935295950474929, 2526377173424697820060353486656610660515990570815979520000000], 0, Rational[-222064082834050351792146883461654210383, 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> b </mi> <annotation-xml encoding='MathML-Content'> <ci> MathieuCharacteristicB </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> 52492329667 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 8 </mn> </msup> </mrow> <mn> 22716763094823469056000 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 9604120067 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 10 </mn> </msup> </mrow> <mn> 6088918573525228742246400 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 52131336111051551 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 12 </mn> </msup> </mrow> <mn> 343105787905984995846250718822400000 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 3037944758311201111 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 14 </mn> </msup> </mrow> <mn> 19065016210783962279192767442085478400000 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 688644321431203907962783243 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 16 </mn> </msup> </mrow> <mn> 793447490813706069985104693586949714944720896000000 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 2113914045440842540935295950474929 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 18 </mn> </msup> </mrow> <mn> 2526377173424697820060353486656610660515990570815979520000000 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 222064082834050351792146883461654210383 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 20 </mn> </msup> </mrow> <mn> 834262291310042453898585976646535297604118819087309409878016000000000 </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'> 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'> -52492329667 <sep /> 22716763094823469056000 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 9604120067 <sep /> 6088918573525228742246400 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> -52131336111051551 <sep /> 343105787905984995846250718822400000 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 3037944758311201111 <sep /> 19065016210783962279192767442085478400000 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> -688644321431203907962783243 <sep /> 793447490813706069985104693586949714944720896000000 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 2113914045440842540935295950474929 <sep /> 2526377173424697820060353486656610660515990570815979520000000 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> -222064082834050351792146883461654210383 <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> MathieuCharacteristicB </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'> -52492329667 <sep /> 22716763094823469056000 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 9604120067 <sep /> 6088918573525228742246400 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> -52131336111051551 <sep /> 343105787905984995846250718822400000 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 3037944758311201111 <sep /> 19065016210783962279192767442085478400000 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> -688644321431203907962783243 <sep /> 793447490813706069985104693586949714944720896000000 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 2113914045440842540935295950474929 <sep /> 2526377173424697820060353486656610660515990570815979520000000 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> -222064082834050351792146883461654210383 <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["MathieuCharacteristicB", "[", 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["$CellContext`q", "6"]]], "-", RowBox[List[FractionBox["52492329667", "22716763094823469056000"], " ", SuperscriptBox["$CellContext`q", "8"]]], "+", RowBox[List[FractionBox["9604120067", "6088918573525228742246400"], " ", SuperscriptBox["$CellContext`q", "10"]]], "-", RowBox[List[FractionBox["52131336111051551", "343105787905984995846250718822400000"], " ", SuperscriptBox["$CellContext`q", "12"]]], "+", RowBox[List[FractionBox["3037944758311201111", "19065016210783962279192767442085478400000"], " ", SuperscriptBox["$CellContext`q", "14"]]], "-", RowBox[List[FractionBox["688644321431203907962783243", "793447490813706069985104693586949714944720896000000"], " ", SuperscriptBox["$CellContext`q", "16"]]], "+", RowBox[List[FractionBox["2113914045440842540935295950474929", "2526377173424697820060353486656610660515990570815979520000000"], " ", SuperscriptBox["$CellContext`q", "18"]]], "-", RowBox[List[FractionBox["222064082834050351792146883461654210383", "834262291310042453898585976646535297604118819087309409878016000000000"], " ", SuperscriptBox["$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[-52492329667, 22716763094823469056000], 0, Rational[9604120067, 6088918573525228742246400], 0, Rational[-52131336111051551, 343105787905984995846250718822400000], 0, Rational[3037944758311201111, 19065016210783962279192767442085478400000], 0, Rational[-688644321431203907962783243, 793447490813706069985104693586949714944720896000000], 0, Rational[2113914045440842540935295950474929, 2526377173424697820060353486656610660515990570815979520000000], 0, Rational[-222064082834050351792146883461654210383, 834262291310042453898585976646535297604118819087309409878016000000000]], 0, 21, 1], Rule[Editable, False]]]]]]










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





2001-10-29





© 1998- Wolfram Research, Inc.