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variants of this functions
GegenbauerC






Mathematica Notation

Traditional Notation









Hypergeometric Functions > GegenbauerC[nu,lambda,z] > Operations > Orthogonality, completeness, and Fourier expansions





http://functions.wolfram.com/07.14.25.0007.01









  


  










Input Form





f[x] == Sum[Subscript[c, n] Subscript[\[Psi], n][x], {n, 0, Infinity}] /; Subscript[c, n] == Integrate[Subscript[\[Psi], n][t] f[t], {t, -1, 1}] && Subscript[\[Psi], n][x] == Sqrt[(n! (\[Lambda] + n) Gamma[\[Lambda]]^2)/ (Pi 2^(1 - 2 \[Lambda]) Gamma[2 \[Lambda] + n])] (1 - x^2)^((2 \[Lambda] - 1)/4) GegenbauerC[n, \[Lambda], x] && -1 < x < 1










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)





2001-10-29