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variants of this functions
GegenbauerC




Mathematica Notation

Traditional Notation









Polynomials > GegenbauerC[n,lambda,z] > Summation > Infinite summation





http://functions.wolfram.com/05.09.23.0007.01









  


  








Input Form





Sum[(Pochhammer[\[Lambda], n]/Pochhammer[2 \[Lambda], n]) GegenbauerC[n, \[Lambda], z] w^n, {n, 0, Infinity}] == (1 - w z)^\[Lambda] Hypergeometric2F1[\[Lambda]/2, (\[Lambda] + 1)/2, \[Lambda] + 1/2, ((z^2 - 1) w^2)/(1 - w z)^2] /; -1 < z < 1 && Abs[w] < 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