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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 generic point z==z0





http://functions.wolfram.com/11.09.06.0003.01









  


  










Input Form





SpheroidalQS[\[Nu], \[Mu], \[Gamma], z] \[Proportional] SpheroidalQS[\[Nu], \[Mu], \[Gamma], Subscript[z, 0]] + SpheroidalQSPrime[\[Nu], \[Mu], \[Gamma], Subscript[z, 0]] (z - Subscript[z, 0]) - (1/(2 (-1 + Subscript[z, 0]^2)^2)) (2 SpheroidalQSPrime[\[Nu], \[Mu], \[Gamma], Subscript[z, 0]] Subscript[z, 0] (-1 + Subscript[z, 0]^2) + SpheroidalQS[\[Nu], \[Mu], \[Gamma], Subscript[z, 0]] (-\[Mu]^2 - SpheroidalEigenvalue[\[Nu], \[Mu], \[Gamma]] (-1 + Subscript[z, 0]^2) + \[Gamma]^2 (-1 + Subscript[z, 0]^2)^2)) (z - Subscript[z, 0])^2 + (1/(6 (-1 + Subscript[z, 0]^2)^3)) ((-SpheroidalQSPrime[\[Nu], \[Mu], \[Gamma], Subscript[z, 0]]) (-1 + Subscript[z, 0]^2) (-2 + \[Gamma]^2 - \[Mu]^2 - 2 (3 + \[Gamma]^2) Subscript[z, 0]^2 + \[Gamma]^2 Subscript[z, 0]^4 - SpheroidalEigenvalue[\[Nu], \[Mu], \[Gamma]] (-1 + Subscript[z, 0]^2)) + 2 SpheroidalQS[\[Nu], \[Mu], \[Gamma], Subscript[z, 0]] Subscript[z, 0] (-3 \[Mu]^2 - 2 SpheroidalEigenvalue[\[Nu], \[Mu], \[Gamma]] (-1 + Subscript[z, 0]^2) + \[Gamma]^2 (-1 + Subscript[z, 0]^2)^2)) (z - Subscript[z, 0])^3 + \[Ellipsis] /; (z -> Subscript[z, 0])










Standard Form





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MathML Form







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Rule Form





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





2007-05-02