Indefinite $q$-integrals from a method using $q$-Ricatti equations
Classical Analysis and ODEs
2022-03-04 v1
Abstract
Earlier work introduced a method for obtaining indefinite -integrals of -special functions from the second-order linear -difference equations that define them. In this paper, we reformulate the method in terms of -Riccati equations, which are nonlinear and first order. We derive -integrals using fragments of these Riccati equations, and here only two specific fragment types are examined in detail. The results presented here are for -Airy function, Ramanujan function, Jackson -Bessel functions, discrete -Hermite polynomials, -Laguerre polynomials, Stieltjes-Wigert polynomial, little -Legendre, and big -Legendre polynomials.
Cite
@article{arxiv.2203.01739,
title = {Indefinite $q$-integrals from a method using $q$-Ricatti equations},
author = {G. E. Heragy and Z. S. I. Mansour and K. M. Oraby},
journal= {arXiv preprint arXiv:2203.01739},
year = {2022}
}