TY - JOUR
A2 - Petit, Franck
AU - Ernst, Thomas
PY - 2013
DA - 2013/03/20
TI - -Pascal and -Wronskian Matrices with Implications to -Appell Polynomials
SP - 450481
VL - 2013
AB - 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.
SN - 2090-9837
UR - https://doi.org/10.1155/2013/450481
DO - 10.1155/2013/450481
JF - Journal of Discrete Mathematics
PB - Hindawi Publishing Corporation
KW -
ER -