A characterization of the exponential symmetric Sheffer sequences. Issue 12 (1st December 2020)

• Record Type: Journal Article
• Authors: Wang, Weiping; Zhang, Ke
• Is Part Of: Integral transforms and special functions. Volume 31:Issue 12(2020)
• Page Start: 955
• Page End: 965
• Publication Date: 2020-12-01
• Subjects: Riordan arrays -- Sheffer sequences -- symmetric polynomials -- combinatorial identities; 05A19 -- 11B83 -- 11C99 -- 33C47; Integral transforms -- Periodicals; Transcendental functions -- Periodicals; Transformations (Mathematics) -- Periodicals; Calculus, Integral -- Periodicals; 515
• DOI: 10.1080/10652469.2020.1763984
• Languages: English
• ISSNs: 1065-2469

Abstract

ABSTRACT: A polynomial sequence ( s n ( x ) ) n ∈ N is symmetric, or self-dual, if s n ( m ) = s m ( n ) for all m, n = 0, 1, 2, … . In this paper, we give the characterization of the exponential symmetric Sheffer sequences with weight sequences, and show that all the symmetric Sheffer sequences with weight ( λ n ), ( ⟨ λ ⟩ n ) or ( ( λ ) n ) are in fact constant multiples of the Charlier polynomial sequence, the Meixner polynomial sequence, or the Krawtchouk polynomial sequence, respectively, where ⟨ λ ⟩ n are the rising factorials, and ( λ ) n are the falling factorials.