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New $U$-Bernoulli, $U$-Euler and $U$-Genocchi polynomials and their matrices

2023; Vasyl Stefanyk Prycarpathian National University; Volume: 15; Issue: 2 Linguagem: Inglês

10.15330/cmp.15.2.449-467

2313-0210

William Ramírez, Daniel Bedoya, Alejandro Urieles, Clemente Cesarano, M.J. Ortega,

Algebraic structures and combinatorial models

In this paper, we introduce the $U$-Bernoulli, $U$-Euler, and $U$-Genocchi polynomials, their numbers, and their relationship with the Riemann zeta function. We also derive the Apostol-type generalizations to obtain some of their algebraic and differential properties. We introduce generalized $U$-Bernoulli, $U$-Euler and $U$-Genocchi polynomial Pascal-type matrix. We deduce some product formulas related to this matrix. Furthermore, we establish some explicit expressions for the $U$-Bernoulli, $U$-Euler, and $U$-Genocchi polynomial matrices, which involves the generalized Pascal matrix.