Some extensions of Bateman's product formulas for the Jacobi polynomials
Date
2009-09-24T22:53:17Z
Authors
Chen, Ming-Po
Srivastava, H.M.
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Abstract
The authors derive generalizations of some remarkable product formulas of Harry Bateman (1882-1946) for the classical Jacobi polynomials. They also show how the results considered here would lead to various families of linear, bilinear, and bilateral generating functions for the Jacobi and related polynomials.
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Keywords
product formulas, Jacobi polynomials, generating functions, series inversion, linearization formula, Gaussian hypergeometric function, hypergeometric identity, quadratic transformation, Appell functions, polynomial expansions, complex sequence, Dixon's summation theorem, Clausenian hypergeometric series, polynomial identity, reduction formula