Some families of generating functions associated with orthogonal polynomials and other higher transcendental functions

Date

2022

Authors

Srivastava, H.M.

Journal Title

Journal ISSN

Volume Title

Publisher

Mathematics

Abstract

In this invited survey-cum-expository review article, we present a brief and comprehensive account of some general families of linear and bilinear generating functions which are associated with orthogonal polynomials and such other higher transcendental functions as (for example) hypergeometric functions and hypergeometric polynomials in one, two and more variables. Many of the results as well as the methods and techniques used for their derivations, which are presented here, are intended to provide incentive and motivation for further research on the subject investigated in this article.

Description

Keywords

linear and bilinear generating functions, orthogonal polynomials, Jacobi, Laguerre and Hermite polynomials, Bessel polynomials, higher transcendental functions, Lagrange's expansion theorem, Bailey's bilinear generating function, Hille-Hardy formula, Mehler's formula, operational techniques, Laplace and inverse Laplace transforms, Riemann-Liouville fractional derivative, hypergeometric functions, hypergeometric polynomials

Citation

Srivastava, H. M. (2022). “Some families of generating functions associated with orthogonal polynomials and other higher transcendental functions.” Mathematics, 10(20), 3730. https://doi.org/10.3390/math10203730