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SpheroidalS2Prime






Mathematica Notation

Traditional Notation









Mathieu and Spheroidal Functions > SpheroidalS2Prime[nu,mu,gamma,z] > Differential equations > Ordinary linear differential equations and wronskians > For the direct function itself





http://functions.wolfram.com/11.15.13.0009.01









  


  










Input Form





(1 - a^2 r^(2 z)) Derivative[2][w][z] + (-Log[r] - a^2 r^(2 z) Log[r] - 2 Log[s] + 2 a^2 r^(2 z) Log[s]) Derivative[1][w][z] + (a^2 r^(2 z) Log[r]^2 SpheroidalEigenvalue[\[Nu], \[Mu], \[Gamma]] + (1/(-1 + a^2 r^(2 z))) ((-a^2) r^(2 z) (-\[Mu]^2 + (-1 + a^2 r^(2 z))^2 \[Gamma]^2) Log[r]^2 + (-1 + a^4 r^(4 z)) Log[r] Log[s] - (-1 + a^2 r^(2 z))^2 Log[s]^2)) w[z] == 0 /; w[z] == Subscript[c, 1] s^z SpheroidalS2Prime[\[Nu], \[Mu], \[Gamma], a r^z] + Subscript[c, 2] s^z SpheroidalS1Prime[\[Nu], \[Mu], \[Gamma], a r^z]










Standard Form





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MathML Form







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</ci> <ci> &#956; </ci> <ci> &#947; </ci> <apply> <times /> <ci> a </ci> <apply> <power /> <ci> r </ci> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <ci> Subscript </ci> <ci> c </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> s </ci> <ci> z </ci> </apply> <apply> <ci> SpheroidalS1Prime </ci> <ci> &#957; </ci> <ci> &#956; </ci> <ci> &#947; </ci> <apply> <times /> <ci> a </ci> <apply> <power /> <ci> r </ci> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2007-05-02