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variants of this functions
JacobiP




Mathematica Notation

Traditional Notation









Polynomials > JacobiP[n,a,b,z] > Generating functions





http://functions.wolfram.com/05.06.11.0002.01









  


  








Input Form





JacobiP[n, \[Alpha], \[Beta], z] == SeriesTerm[((Pochhammer[1 + \[Alpha], n] Pochhammer[1 + \[Beta], n])/ (Pochhammer[a, n] Pochhammer[1 + \[Alpha] + \[Beta] - a, n])) Hypergeometric2F1[a, 1 + \[Alpha] + \[Beta] - a, 1 + \[Alpha], (1/2) (1 - t - Sqrt[1 - 2 z t + t^2])] Hypergeometric2F1[a, 1 + \[Alpha] + \[Beta] - a, 1 + \[Beta], (1/2) (1 + t - Sqrt[1 - 2 z t + t^2])], {t, 0, n}] /; -1 < z < 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)





2002-12-18