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SpheroidalQS




Mathematica Notation

Traditional Notation









Mathieu and Spheroidal Functions > SpheroidalQS[nu,mu,gamma,z] > Series representations > Generalized power series > Expansions at z==0





http://functions.wolfram.com/11.09.06.0005.01









  


  








Input Form





SpheroidalQS[\[Nu], \[Mu], \[Gamma], z] \[Proportional] SpheroidalQS[\[Nu], \[Mu], \[Gamma], 0] + z SpheroidalQSPrime[\[Nu], \[Mu], \[Gamma], 0] - (1/2) (\[Gamma]^2 - \[Mu]^2 + SpheroidalEigenvalue[\[Nu], \[Mu], \[Gamma]]) SpheroidalQS[\[Nu], \[Mu], \[Gamma], 0] z^2 + (1/6) (2 SpheroidalQSPrime[\[Nu], \[Mu], \[Gamma], 0] - (\[Gamma]^2 - \[Mu]^2 + SpheroidalEigenvalue[\[Nu], \[Mu], \[Gamma]]) SpheroidalQSPrime[\[Nu], \[Mu], \[Gamma], 0]) z^3 + \[Ellipsis] /; (z -> 0)








Standard Form





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MathML Form







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</mo> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <semantics> <mo> &#8594; </mo> <annotation encoding='Mathematica'> &quot;\[Rule]&quot; </annotation> </semantics> <mn> 0 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <ci> Proportional </ci> <apply> <ci> SpheroidalQS </ci> <ci> &#957; </ci> <ci> &#956; </ci> <ci> &#947; </ci> <ci> z </ci> </apply> <apply> <plus /> <apply> <ci> SpheroidalQS </ci> <ci> &#957; </ci> <ci> &#956; </ci> <ci> &#947; </ci> <cn type='integer'> 0 </cn> </apply> <apply> <times /> <apply> <ci> SpheroidalQSPrime </ci> <ci> &#957; </ci> <ci> &#956; </ci> <ci> &#947; </ci> <cn type='integer'> 0 </cn> </apply> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <plus /> <apply> <power /> <ci> &#947; </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> &#956; </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <ci> SpheroidalEigenvalue </ci> <ci> &#957; </ci> <ci> &#956; </ci> <ci> &#947; </ci> </apply> </apply> <apply> <ci> SpheroidalQS </ci> <ci> &#957; </ci> <ci> &#956; </ci> <ci> &#947; </ci> <cn type='integer'> 0 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 6 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <ci> SpheroidalQSPrime </ci> <ci> &#957; </ci> <ci> &#956; </ci> <ci> &#947; </ci> <cn type='integer'> 0 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <plus /> <apply> <power /> <ci> &#947; </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> &#956; </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <ci> SpheroidalEigenvalue </ci> <ci> &#957; </ci> <ci> &#956; </ci> <ci> &#947; </ci> </apply> </apply> <apply> <ci> SpheroidalQSPrime </ci> <ci> &#957; </ci> <ci> &#956; </ci> <ci> &#947; </ci> <cn type='integer'> 0 </cn> </apply> </apply> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <ci> &#8230; </ci> </apply> </apply> <apply> <ci> Rule </ci> <ci> z </ci> <cn type='integer'> 0 </cn> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2007-05-02