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variants of this functions
GegenbauerC




Mathematica Notation

Traditional Notation









Hypergeometric Functions > GegenbauerC[nu,z] > Differential equations > Ordinary linear differential equations and wronskians > For the direct function itself > With respect to z





http://functions.wolfram.com/07.13.13.0023.01









  


  








Input Form





(-1 + a^2 r^(2 z)) Derivative[2][w][z] + (Log[r] - 2 (-1 + a^2 r^(2 z)) Log[s]) Derivative[1][w][z] + ((-Log[s]) (Log[r] + Log[s]) + a^2 r^(2 z) ((-\[Nu]^2) Log[r]^2 + Log[s]^2)) w[z] == 0 /; w[z] == Subscript[c, 1] s^z GegenbauerC[\[Nu], a r^z] + Subscript[c, 2] s^z Sqrt[1 - a^2 r^(2 z)] ChebyshevU[-1 + \[Nu], a r^z]








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