New $U$-Bernoulli, $U$-Euler and $U$-Genocchi polynomials and their matrices
Keywords:
$U$-Bernoulli polynomial, $U$-Euler polynomial, generalized $U$-Bernoulli polynomial, generalized $U$-Euler polynomial, $U$-Bernoulli polynomials matrix, $U$-Euler polynomials matrix, Pascal matrix
Published online:
2023-11-21
Abstract
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.
How to Cite
(1)
Ramírez, W.; Bedoya, D.; Urieles, A.; Cesarano, C.; Ortega, M. New $U$-Bernoulli, $U$-Euler and $U$-Genocchi Polynomials and Their Matrices. Carpathian Math. Publ. 2023, 15, 449-467.