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SpheroidalPS






Mathematica Notation

Traditional Notation









Mathieu and Spheroidal Functions > SpheroidalPS[nu,mu,gamma,z] > Series representations > Other series representations





http://functions.wolfram.com/11.08.06.0007.01









  


  










Input Form





SpheroidalPS[\[Nu], \[Mu], \[Gamma], z] == Sum[(-1)^k \[Alpha][\[Nu], \[Mu], \[Gamma], k] LegendreP[\[Nu] + 2 k, \[Mu], 2, z], {k, -Infinity, Infinity}] /; A[\[Nu], \[Mu], \[Gamma], k] \[Alpha][\[Nu], \[Mu], \[Gamma], k - 1] + (B[\[Nu], \[Mu], \[Gamma], k] - SpheroidalEigenvalue[\[Nu], \[Mu], \[Gamma]]) \[Alpha][\[Nu], \[Mu], \[Gamma], k] + C[\[Nu], \[Mu], \[Gamma], k] \[Alpha][\[Nu], \[Mu], \[Gamma], k + 1] && A[\[Nu], \[Mu], \[Gamma], k] == (-\[Gamma]^2) (((\[Nu] - \[Mu] + 2 k - 1) (\[Nu] - \[Mu] + 2 k))/ ((2 \[Nu] + 4 k - 3) (2 \[Nu] + 4 k - 1))) && B[\[Nu], \[Mu], \[Gamma], k] == (\[Nu] + 2 k) (\[Nu] + 2 k + 1) - (2 \[Gamma]^2 ((\[Nu] + 2 k) (\[Nu] + 2 k + 1) + \[Mu]^2 - 1))/ ((2 \[Nu] + 4 k - 1) (2 \[Nu] + 4 k + 3)) && C[\[Nu], \[Mu], \[Gamma], k] == -((\[Gamma]^2 (\[Nu] + \[Mu] + 2 k + 1) (\[Nu] + \[Mu] + 2 k + 2))/ ((2 \[Nu] + 4 k + 3) (2 \[Nu] + 4 k + 5)))










Standard Form





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MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <msub> <semantics> <mi> M </mi> <annotation encoding='Mathematica'> TagBox[&quot;M&quot;, WhittakerM] </annotation> </semantics> <mrow> <mi> &#957; </mi> <mo> , </mo> <mi> &#956; </mi> </mrow> </msub> <mo> ( </mo> <mn> 0 </mn> <mo> ) </mo> </mrow> <mo> &#63449; </mo> <mn> 0 </mn> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> Re </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> &#956; </mi> <mo> ) </mo> </mrow> <mo> &gt; </mo> <mrow> <mo> - </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <ci> WhittakerM </ci> <ci> &#957; </ci> <ci> &#956; </ci> <cn type='integer'> 0 </cn> </apply> <cn type='integer'> 0 </cn> </apply> <apply> <gt /> <apply> <real /> <ci> &#956; </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2007-05-02





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