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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/11.05.06.0001.01









  


  










Input Form





MathieuCharacteristicA[r, q] \[Proportional] SeriesData[$CellContext`q, 0, {$CellContext`r^2, 0, Rational[1, 2]/((-1 + $CellContext`r) (1 + $CellContext`r)), 0, (Rational[1, 32] (7 + 5 $CellContext`r^2))/ ((-2 + $CellContext`r) (-1 + $CellContext`r)^3 (1 + $CellContext`r)^3 (2 + $CellContext`r)), 0, (Rational[1, 64] (29 + 58 $CellContext`r^2 + 9 $CellContext`r^4))/((-3 + $CellContext`r) (-2 + $CellContext`r) (-1 + $CellContext`r)^5 (1 + $CellContext`r)^5 (2 + $CellContext`r) (3 + $CellContext`r)), 0, (Rational[1, 8192] (274748 + 827565 $CellContext`r^2 + 64228 $CellContext`r^4 - 140354 $CellContext`r^6 + 9144 $CellContext`r^8 + 1469 $CellContext`r^10))/ ((-4 + $CellContext`r) (-3 + $CellContext`r) (-2 + $CellContext`r)^3 (-1 + $CellContext`r)^7 (1 + $CellContext`r)^7 (2 + $CellContext`r)^3 (3 + $CellContext`r) (4 + $CellContext`r)), 0, (Rational[1, 16384] (4453452 + 20651309 $CellContext`r^2 + 13541915 $CellContext`r^4 - 2844430 $CellContext`r^6 - 1039598 $CellContext`r^8 + 69361 $CellContext`r^10 + 4471 $CellContext`r^12))/((-5 + $CellContext`r) (-4 + $CellContext`r) (-3 + $CellContext`r) (-2 + $CellContext`r)^3 (-1 + $CellContext`r)^9 (1 + $CellContext`r)^9 (2 + $CellContext`r)^3 (3 + $CellContext`r) (4 + $CellContext`r) (5 + $CellContext`r))}, 0, 11, 1] /; !(Element[r, Integers] && -10 <= r <= 10)










Standard Form





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MathML Form







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</mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 7 </mn> </msup> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 3 </mn> </msup> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 3 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 4 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 4471 </mn> <mo> &#8290; </mo> <msup> <mi> r </mi> <mn> 12 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 69361 </mn> <mo> &#8290; </mo> <msup> <mi> r </mi> <mn> 10 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 1039598 </mn> <mo> &#8290; </mo> <msup> <mi> r </mi> <mn> 8 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 2844430 </mn> <mo> &#8290; </mo> <msup> <mi> r </mi> <mn> 6 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 13541915 </mn> <mo> &#8290; </mo> <msup> <mi> r </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 20651309 </mn> <mo> &#8290; </mo> <msup> <mi> r </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mn> 4453452 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 10 </mn> </msup> </mrow> <mo> ) </mo> </mrow> <mo> / </mo> <mrow> <mo> ( </mo> <mrow> <mn> 16384 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> - </mo> <mn> 5 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> - </mo> <mn> 4 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> - </mo> <mn> 3 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 3 </mn> </msup> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 9 </mn> </msup> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 9 </mn> </msup> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 3 </mn> </msup> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 3 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 4 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 5 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mi> O </mi> <mo> &#8289; </mo> <mo> ( </mo> <msup> <mi> q </mi> <mn> 11 </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> <apply> <power /> <ci> $CellContext`r </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> 0 </cn> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <power /> <apply> <plus /> <cn type='integer'> -1 </cn> <ci> $CellContext`r </ci> </apply> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <ci> $CellContext`r </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 0 </cn> <apply> <times /> <cn type='rational'> 1 <sep /> 32 </cn> <apply> <power /> <apply> <plus /> <cn type='integer'> -2 </cn> <ci> $CellContext`r </ci> </apply> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> -1 </cn> <ci> $CellContext`r </ci> </apply> <cn type='integer'> -3 </cn> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <ci> $CellContext`r </ci> </apply> <cn type='integer'> -3 </cn> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> 2 </cn> 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Rule Form





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





2001-10-29