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/11.05.06.0007.01









  


  










Input Form





MathieuCharacteristicA[5, q] \[Proportional] SeriesData[$CellContext`q, 0, {25, 0, Rational[1, 48], 0, Rational[11, 774144], Rational[1, 147456], Rational[37, 891813888], Rational[-7, 339738624], Rational[63439, 201364441399296], Rational[-1, 2130840649728], Rational[-60609509, 5799295912299724800], Rational[-6655, 88370223425519616], Rational[105674803279, 2400630141488295680409600], Rational[-5574517, 4988322371923731283968], Rational[-16772318839, 395075131856359517690265600], Rational[65998078949, 2394394738523391016304640000], Rational[670043657712623, 3247054871864845067146864392929280], Rational[-6770772278721223, 49062642294661120520076247695360000], Rational[240333014990212253, 56109108185824522760297816709817958400], Rational[120574357589460233, 452161311387596886713022698760437760000], Rational[-50669327402196350835443, 565579810513111189423801992434965020672000000]}, 0, 21, 1]










Standard Form





Cell[BoxData[RowBox[List[RowBox[List["MathieuCharacteristicA", "[", RowBox[List["5", ",", "q"]], "]"]], "\[Proportional]", InterpretationBox[RowBox[List["25", "+", FractionBox[SuperscriptBox["q", "2"], "48"], "+", FractionBox[RowBox[List["11", " ", SuperscriptBox["q", "4"]]], "774144"], "+", FractionBox[SuperscriptBox["q", "5"], "147456"], "+", FractionBox[RowBox[List["37", " ", SuperscriptBox["q", "6"]]], "891813888"], "-", FractionBox[RowBox[List["7", " ", SuperscriptBox["q", "7"]]], "339738624"], "+", FractionBox[RowBox[List["63439", " ", SuperscriptBox["q", "8"]]], "201364441399296"], "-", FractionBox[SuperscriptBox["q", "9"], "2130840649728"], "-", FractionBox[RowBox[List["60609509", " ", SuperscriptBox["q", "10"]]], "5799295912299724800"], "-", FractionBox[RowBox[List["6655", " ", SuperscriptBox["q", "11"]]], "88370223425519616"], "+", FractionBox[RowBox[List["105674803279", " ", SuperscriptBox["q", "12"]]], "2400630141488295680409600"], "-", FractionBox[RowBox[List["5574517", " ", SuperscriptBox["q", "13"]]], "4988322371923731283968"], "-", FractionBox[RowBox[List["16772318839", " ", SuperscriptBox["q", "14"]]], "395075131856359517690265600"], "+", FractionBox[RowBox[List["65998078949", " ", SuperscriptBox["q", "15"]]], "2394394738523391016304640000"], "+", FractionBox[RowBox[List["670043657712623", " ", SuperscriptBox["q", "16"]]], "3247054871864845067146864392929280"], "-", FractionBox[RowBox[List["6770772278721223", " ", SuperscriptBox["q", "17"]]], "49062642294661120520076247695360000"], "+", FractionBox[RowBox[List["240333014990212253", " ", SuperscriptBox["q", "18"]]], "56109108185824522760297816709817958400"], "+", FractionBox[RowBox[List["120574357589460233", " ", SuperscriptBox["q", "19"]]], "452161311387596886713022698760437760000"], "-", FractionBox[RowBox[List["50669327402196350835443", " ", SuperscriptBox["q", "20"]]], "565579810513111189423801992434965020672000000"], "+", InterpretationBox[SuperscriptBox[RowBox[List["O", "[", "q", "]"]], "21"], SeriesData[$CellContext`q, 0, List[], 0, 21, 1]]]], SeriesData[$CellContext`q, 0, List[25, 0, Rational[1, 48], 0, Rational[11, 774144], Rational[1, 147456], Rational[37, 891813888], Rational[-7, 339738624], Rational[63439, 201364441399296], Rational[-1, 2130840649728], Rational[-60609509, 5799295912299724800], Rational[-6655, 88370223425519616], Rational[105674803279, 2400630141488295680409600], Rational[-5574517, 4988322371923731283968], Rational[-16772318839, 395075131856359517690265600], Rational[65998078949, 2394394738523391016304640000], Rational[670043657712623, 3247054871864845067146864392929280], Rational[-6770772278721223, 49062642294661120520076247695360000], Rational[240333014990212253, 56109108185824522760297816709817958400], Rational[120574357589460233, 452161311387596886713022698760437760000], Rational[-50669327402196350835443, 565579810513111189423801992434965020672000000]], 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> 5 </mn> </msub> <mo> ( </mo> <mi> q </mi> <mo> ) </mo> </mrow> <mo> &#8733; </mo> <semantics> <mrow> <mn> 25 </mn> <mo> + </mo> <mfrac> <msup> <mi> q </mi> <mn> 2 </mn> </msup> <mn> 48 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 11 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 4 </mn> </msup> </mrow> <mn> 774144 </mn> </mfrac> <mo> + </mo> <mfrac> <msup> <mi> q </mi> <mn> 5 </mn> </msup> <mn> 147456 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 37 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 6 </mn> </msup> </mrow> <mn> 891813888 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 7 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 7 </mn> </msup> </mrow> <mn> 339738624 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 63439 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 8 </mn> </msup> </mrow> <mn> 201364441399296 </mn> </mfrac> <mo> - </mo> <mfrac> <msup> <mi> q </mi> <mn> 9 </mn> </msup> <mn> 2130840649728 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 60609509 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 10 </mn> </msup> </mrow> <mn> 5799295912299724800 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 6655 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 11 </mn> </msup> </mrow> <mn> 88370223425519616 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 105674803279 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 12 </mn> </msup> </mrow> <mn> 2400630141488295680409600 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 5574517 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 13 </mn> </msup> </mrow> <mn> 4988322371923731283968 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 16772318839 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 14 </mn> </msup> </mrow> <mn> 395075131856359517690265600 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 65998078949 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 15 </mn> </msup> </mrow> <mn> 2394394738523391016304640000 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 670043657712623 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 16 </mn> </msup> </mrow> <mn> 3247054871864845067146864392929280 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 6770772278721223 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 17 </mn> </msup> </mrow> <mn> 49062642294661120520076247695360000 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 240333014990212253 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 18 </mn> </msup> </mrow> <mn> 56109108185824522760297816709817958400 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 120574357589460233 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 19 </mn> </msup> </mrow> <mn> 452161311387596886713022698760437760000 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 50669327402196350835443 </mn> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 20 </mn> </msup> </mrow> <mn> 565579810513111189423801992434965020672000000 </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'> 25 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 1 <sep /> 48 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 11 <sep /> 774144 </cn> <cn type='rational'> 1 <sep /> 147456 </cn> <cn type='rational'> 37 <sep /> 891813888 </cn> <cn type='rational'> -7 <sep /> 339738624 </cn> <cn type='rational'> 63439 <sep /> 201364441399296 </cn> <cn type='rational'> -1 <sep /> 2130840649728 </cn> <cn type='rational'> -60609509 <sep /> 5799295912299724800 </cn> <cn type='rational'> -6655 <sep /> 88370223425519616 </cn> <cn type='rational'> 105674803279 <sep /> 2400630141488295680409600 </cn> <cn type='rational'> -5574517 <sep /> 4988322371923731283968 </cn> <cn type='rational'> -16772318839 <sep /> 395075131856359517690265600 </cn> <cn type='rational'> 65998078949 <sep /> 2394394738523391016304640000 </cn> <cn type='rational'> 670043657712623 <sep /> 3247054871864845067146864392929280 </cn> <cn type='rational'> -6770772278721223 <sep /> 49062642294661120520076247695360000 </cn> <cn type='rational'> 240333014990212253 <sep /> 56109108185824522760297816709817958400 </cn> <cn type='rational'> 120574357589460233 <sep /> 452161311387596886713022698760437760000 </cn> <cn type='rational'> -50669327402196350835443 <sep /> 565579810513111189423801992434965020672000000 </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'> 5 </cn> <ci> q </ci> </apply> <apply> <ci> SeriesData </ci> <ci> $CellContext`q </ci> <cn type='integer'> 0 </cn> <list> <cn type='integer'> 25 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 1 <sep /> 48 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 11 <sep /> 774144 </cn> <cn type='rational'> 1 <sep /> 147456 </cn> <cn type='rational'> 37 <sep /> 891813888 </cn> <cn type='rational'> -7 <sep /> 339738624 </cn> <cn type='rational'> 63439 <sep /> 201364441399296 </cn> <cn type='rational'> -1 <sep /> 2130840649728 </cn> <cn type='rational'> -60609509 <sep /> 5799295912299724800 </cn> <cn type='rational'> -6655 <sep /> 88370223425519616 </cn> <cn type='rational'> 105674803279 <sep /> 2400630141488295680409600 </cn> <cn type='rational'> -5574517 <sep /> 4988322371923731283968 </cn> <cn type='rational'> -16772318839 <sep /> 395075131856359517690265600 </cn> <cn type='rational'> 65998078949 <sep /> 2394394738523391016304640000 </cn> <cn type='rational'> 670043657712623 <sep /> 3247054871864845067146864392929280 </cn> <cn type='rational'> -6770772278721223 <sep /> 49062642294661120520076247695360000 </cn> <cn type='rational'> 240333014990212253 <sep /> 56109108185824522760297816709817958400 </cn> <cn type='rational'> 120574357589460233 <sep /> 452161311387596886713022698760437760000 </cn> <cn type='rational'> -50669327402196350835443 <sep /> 565579810513111189423801992434965020672000000 </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["5", ",", "q_"]], "]"]], "]"]], "\[RuleDelayed]", InterpretationBox[RowBox[List["25", "+", RowBox[List[FractionBox["1", "48"], " ", SuperscriptBox["$CellContext`q", "2"]]], "+", RowBox[List[FractionBox["11", "774144"], " ", SuperscriptBox["$CellContext`q", "4"]]], "+", RowBox[List[FractionBox["1", "147456"], " ", SuperscriptBox["$CellContext`q", "5"]]], "+", RowBox[List[FractionBox["37", "891813888"], " ", SuperscriptBox["$CellContext`q", "6"]]], "-", RowBox[List[FractionBox["7", "339738624"], " ", SuperscriptBox["$CellContext`q", "7"]]], "+", RowBox[List[FractionBox["63439", "201364441399296"], " ", SuperscriptBox["$CellContext`q", "8"]]], "-", RowBox[List[FractionBox["1", "2130840649728"], " ", SuperscriptBox["$CellContext`q", "9"]]], "-", RowBox[List[FractionBox["60609509", "5799295912299724800"], " ", SuperscriptBox["$CellContext`q", "10"]]], "-", RowBox[List[FractionBox["6655", "88370223425519616"], " ", SuperscriptBox["$CellContext`q", "11"]]], "+", RowBox[List[FractionBox["105674803279", "2400630141488295680409600"], " ", SuperscriptBox["$CellContext`q", "12"]]], "-", RowBox[List[FractionBox["5574517", "4988322371923731283968"], " ", SuperscriptBox["$CellContext`q", "13"]]], "-", RowBox[List[FractionBox["16772318839", "395075131856359517690265600"], " ", SuperscriptBox["$CellContext`q", "14"]]], "+", RowBox[List[FractionBox["65998078949", "2394394738523391016304640000"], " ", SuperscriptBox["$CellContext`q", "15"]]], "+", RowBox[List[FractionBox["670043657712623", "3247054871864845067146864392929280"], " ", SuperscriptBox["$CellContext`q", "16"]]], "-", RowBox[List[FractionBox["6770772278721223", "49062642294661120520076247695360000"], " ", SuperscriptBox["$CellContext`q", "17"]]], "+", RowBox[List[FractionBox["240333014990212253", "56109108185824522760297816709817958400"], " ", SuperscriptBox["$CellContext`q", "18"]]], "+", RowBox[List[FractionBox["120574357589460233", "452161311387596886713022698760437760000"], " ", SuperscriptBox["$CellContext`q", "19"]]], "-", RowBox[List[FractionBox["50669327402196350835443", "565579810513111189423801992434965020672000000"], " ", SuperscriptBox["$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[25, 0, Rational[1, 48], 0, Rational[11, 774144], Rational[1, 147456], Rational[37, 891813888], Rational[-7, 339738624], Rational[63439, 201364441399296], Rational[-1, 2130840649728], Rational[-60609509, 5799295912299724800], Rational[-6655, 88370223425519616], Rational[105674803279, 2400630141488295680409600], Rational[-5574517, 4988322371923731283968], Rational[-16772318839, 395075131856359517690265600], Rational[65998078949, 2394394738523391016304640000], Rational[670043657712623, 3247054871864845067146864392929280], Rational[-6770772278721223, 49062642294661120520076247695360000], Rational[240333014990212253, 56109108185824522760297816709817958400], Rational[120574357589460233, 452161311387596886713022698760437760000], Rational[-50669327402196350835443, 565579810513111189423801992434965020672000000]], 0, 21, 1], Rule[Editable, False]]]]]]










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





2001-10-29