A certain method of obtaining bilateral generating functions

✍ Scribed by H.M Srivastava; J.-L Lavoie

• Publisher: Elsevier Science
• Year: 1975
• Weight: 749 KB
• Volume: 78
• Category: Article
• ISSN: 1385-7258
• DOI: 10.1016/1385-7258(75)90002-5

✦ Synopsis

This paper presents a systematic introduction to and several applications of a certain method of obtaining bilinear or bilateral generating relations for a large variety of sequences of special functions.

The main result, given by Theorem 1 below, is shown to apply, for instance, to the Bessel, Brafman, Charlier, Gegenbauer (or ultraspherical), Gould-Hopper, Jacobi, Hermite, Konhauser, Laguerre (or the modified Laguerre)

and Srivastava-Singhal polynomials, while its generalization, given by Theorem 2, would apply to the Lauricella polynomials in several variables and to the familiar Lagrange polynomials which arise in certain problems in statistics. It is also shown how these results can be extended to yield bilateral generating relations for such other special fun&ions as the Bessel functions.