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variants of this functions
GegenbauerC






Mathematica Notation

Traditional Notation









Polynomials > GegenbauerC[n,lambda,z] > Differential equations > Ordinary linear differential equations and wronskians > For the direct function itself





http://functions.wolfram.com/05.09.13.0009.01









  


  










Input Form





Derivative[2][w][z] - (Log[r] + (a^2 r^(2 z) (1 + 2 \[Lambda]) Log[r])/ (1 - a^2 r^(2 z)) + 2 Log[s]) Derivative[1][w][z] + ((1/(-1 + a^2 r^(2 z))) ((-Log[s]) (Log[r] + Log[s]) + a^2 r^(2 z) (n Log[r] + Log[s]) ((-(2 \[Lambda] + n)) Log[r] + Log[s]))) w[z] == 0 /; w[z] == Subscript[c, 1] s^z GegenbauerC[n, \[Lambda], a r^z] + Subscript[c, 2] s^z (1 - a^2 r^(2 z))^((1 - 2 \[Lambda])/4) LegendreQ[n + \[Lambda] - 1/2, 1/2 - \[Lambda], 2, 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