Q-Pascal and q-Wronskian Matrices with Implications to q-Appell Polynomials. (20th March 2013)

• Record Type: Journal Article
• Authors: Ernst, Thomas
• Other Names: Petit Franck Academic Editor.
• Is Part Of: Journal of discrete mathematics. Volume 2013(2013)
• Publication Date: 2013-03-20
• Subjects: Computer science -- Mathematics -- Periodicals; Computer science -- Mathematics; Periodicals; 511.1
• DOI: 10.1155/2013/450481
• Languages: English
• ISSNs: 2090-9837

Abstract

Abstract : We introduce a q -deformation of the Yang and Youn matrix approach for Appell polynomials. This will lead to a powerful machinery for producing new and old formulas for q -Appell polynomials, and in particular for q -Bernoulli and q -Euler polynomials. Furthermore, the q -L -polynomial, anticipated by Ward, can be expressed as a sum of products of q -Bernoulli and q -Euler polynomials. The pseudo q -Appell polynomials, which are first presented in this paper, enable multiple q -analogues of the Yang and Youn formulas. The generalized q -Pascal functional matrix, the q -Wronskian vector of a function, and the vector of q -Appell polynomials together with the q -deformed ϵ matrix multiplication from the authors recent article are the main ingredients in the process. Beyond these results, we give a characterization of q -Appell numbers, improving on Al-Salam 1967. Finally, we find a q -difference equation for the q -Appell polynomial of degree n .