A large family of Dw-semiclassical polynomials of class one. Issue 5 (4th May 2017)

• Record Type: Journal Article
• Authors: Sghaier, M.; Zaatra, M.
• Is Part Of: Integral transforms and special functions. Volume 28:Issue 5(2017)
• Page Start: 386
• Page End: 402
• Publication Date: 2017-05-04
• Subjects: Discrete semiclassical orthogonal polynomials -- difference operator; 33C45 -- 42C05; Integral transforms -- Periodicals; Transcendental functions -- Periodicals; Transformations (Mathematics) -- Periodicals; Calculus, Integral -- Periodicals; 515
• DOI: 10.1080/10652469.2017.1304392
• Languages: English
• ISSNs: 1065-2469

Abstract

ABSTRACT: Letu ( β 0 ) be the regular form fulfilling( u ( β 0 ) ) 2 n + 1 = β 0 ( u ( β 0 ) ) 2 n, n ≥ 0 whereβ 0 is an arbitrary complex number in such a way that forβ 0 = 0 one has the symmetric forms. Recently, the symmetricD w -semiclassical forms (whenβ 0 = 0 ) of classs ≤ 1 are determined whereD w is the divided difference operator. In this paper, we determine all theD w -semiclassical formsu ( β 0 ) of class s =1, whenβ 0 ≠ 0 .