Generating functions for generalized Hermite polynomials associated with parabolic cylinder functions. Issue 5 (3rd May 2020)

• Record Type: Journal Article
• Authors: Shahwan, M. J. S.; Sharif, A. M.; Bin-Saad, Maged G.
• Is Part Of: Integral transforms and special functions. Volume 31:Issue 5(2020)
• Page Start: 383
• Page End: 394
• Publication Date: 2020-05-03
• Subjects: Generalized Hermite polynomials -- parabolic cylinder functions -- generating functions -- Weisnerś group theoretic method -- operational rules; 33C45 -- 33C80; Integral transforms -- Periodicals; Transcendental functions -- Periodicals; Transformations (Mathematics) -- Periodicals; Calculus, Integral -- Periodicals; 515
• DOI: 10.1080/10652469.2019.1697695
• Languages: English
• ISSNs: 1065-2469

Abstract

ABSTRACT: In this article, we first give some basic properties of generalized Hermite polynomials associated with parabolic cylinder functions. We next use Weisnerś group theoretic method and operational rules method to establish new generating functions for these generalized Hermite polynomials. The operational methods we use allow us to obtain unilateral, bilinear and bilateral generating functions by using the same procedure. Applications of generating functions obtained by Weisnerś group theoretic method are discussed.