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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/05.09.13.0005.01









  


  










Input Form





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










Standard Form





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MathML Form







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</ci> </apply> </apply> <cn type='integer'> 2 </cn> <apply> <ci> g </ci> <ci> z </ci> </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