New results on the q-generalized Bernoulli polynomials of level m

Abstract

This paper aims to show new algebraic properties from the q-generalized Bernoulli polynomials B_n^{[m - 1]}(x;q) of level m, as well as some others identities which connect this polynomial class with the q-generalized Bernoulli polynomials of level m, as well as the q-gamma function, and the q-Stirling numbers of the second kind and the q-Bernstein polynomials.

On $q$-hypergeometric Bernoulli polynomials and numbers

“…and studied several of their properties. Another important generalization can be found in [21] but all these generalizations are different from ours.…”

About family Apostol Fubini-Euler type polynomials: Fourier expansions and integral representation

“…We also show some applications that meet this family of Apostol Fubini-Euler type polynomials. On the subject of the Apostol-type polynomials and their various extensions, a remarkably large number of investigations have appeared in the literature, for example, see [1,3,5,6,10,13,[17][18][19][20][21]. The paper is organized as follows.…”

New Approaches to the General Linearization Problem of Jacobi Polynomials Based on Moments and Connection Formulas

“…Special functions are crucial in several disciplines such as mathematical physics and numerical analysis. A large number of researchers are interested in investigating different special functions from numerical and practical points of view; see, for example, [1][2][3].…”