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 Bn[m-1](x;q)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.

Keywords

• q-generalized bernoulli polynomials
• q-gamma function
• q-stirling numbers
• q-bernstein poly-nomials
• 33e12