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variants of this functions
GegenbauerC






Mathematica Notation

Traditional Notation









Polynomials > GegenbauerC[n,lambda,z] > Operations > Orthogonality, completeness, and Fourier expansions





http://functions.wolfram.com/05.09.25.0005.01









  


  










Input Form





Sum[(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]) (Sqrt[(n! (\[Lambda] + n) Gamma[\[Lambda]]^2)/(Pi 2^(1 - 2 \[Lambda]) Gamma[2 \[Lambda] + n])] (1 - y^2)^((2 \[Lambda] - 1)/4) GegenbauerC[n, \[Lambda], y]), {n, 0, Infinity}] == DiracDelta[x - y] /; Re[\[Lambda]] > -(1/2) && \[Lambda] != 0 && -1 < x < 1 && -1 < y < 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