New generating functions for Jacobi and related polynomials

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Abstract

In this paper the authors prove a generalization of certain generating functions for Jacobi and related polynomials, given recently by H. M. Srivastava. The method used is due to Pólya and Szegö, and it is based on Rodrigues' formula for the Jacobi polynomials and Lagrange's expansion theorem. A number of special and limiting cases of the main result will give rise to a class of generating functions for ultraspherical, Laguerre and Bessel polynomials.

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Notices Amer. Math. Soc. 18 (1971), p. 555, Abstract 71T-B83. This work was supported in part by the National Research Council of Canada under Grant A7353.