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