Generalized $q$-Bernoulli polynomials generated by Jackson $q$-Bessel functions

S. Z. Eweis, Zeinab S. I. Mansour

In this paper, we introduce the polynomials $B_{n,\alpha }^{(k)}(x;q)$ generated by a function including Jackson $q$-Bessel functions $J_{\alpha }^{(k)}(x;q)$ $(k=1,2,3),\alpha >-1$. The cases $α=\…