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

2022/01/25 by Eweis, S. Z., Mansour, Zeinab S. I.
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2201.10117

Abstract

In this paper, we introduce the polynomials B^(k)_n,α(x;q) generated by a function including Jackson q-Bessel functions J^(k)_α(x;q) (k=1,2,3), α>-1. The cases α=±(1)/(2) are the q-analogs of Bernoulli and Euler^,s polynomials introduced by Ismail and Mansour for (k=1,2), Mansour and Al-Towalib for (k=3). We study the main properties of these polynomials, their large n degree asymptotics and give their connection coefficients with the q-Laguerre polynomials and little q-Legendre polynomials.

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