Generating functions and a family of special orthogonal polynomials. Issue 1 (2nd January 2018)

• Record Type: Journal Article
• Authors: Sghaier, M.; Khlifi, A.
• Is Part Of: Integral transforms and special functions. Volume 29:Issue 1(2018)
• Page Start: 62
• Page End: 80
• Publication Date: 2018-01-02
• Subjects: Orthogonal polynomials -- generating functions -- quadratic decomposition; 33C45 -- 42C05; Integral transforms -- Periodicals; Transcendental functions -- Periodicals; Transformations (Mathematics) -- Periodicals; Calculus, Integral -- Periodicals; 515
• DOI: 10.1080/10652469.2017.1404595
• Languages: English
• ISSNs: 1065-2469

Abstract

ABSTRACT: In this paper, we use quadratic decomposition to develop a method for constructing generating functions for orthogonal polynomials{ B n } n ≥ 0 verifying the three-term recurrence relation withβ n = ( − 1 ) n c, c ∈ C . As application, we can deduce explicitly the expression for the generating functionB ( x, t ) = ∑ n = 0 + ∞ a n B n ( x ) t n in some well-known semiclassical cases.