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arXiv · 2203.01739

Indefinite $q$-integrals from a method using $q$-Ricatti equations

G. E. Heragy·Z. S. I. Mansour·K. M. Oraby
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Abstract

Earlier work introduced a method for obtaining indefinite $q$-integrals of $q$-special functions from the second-order linear $q$-difference equations that define them. In this paper, we reformulate the method in terms of $q$-Riccati equations, which are nonlinear and first order. We derive $q$-integrals using fragments of these Riccati equations, and here only two specific fragment types are examined in detail. The results presented here are for $q$-Airy function, Ramanujan function, Jackson $q$-Bessel functions, discrete $q$-Hermite polynomials, $q$-Laguerre polynomials, Stieltjes-Wigert polynomial, little $q$-Legendre, and big $q$-Legendre polynomials.

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BibTeXRIS

G. E. Heragy, Z. S. I. Mansour, K. M. Oraby. 2022-03-03. Indefinite $q$-integrals from a method using $q$-Ricatti equations. https://arxiv.org/abs/2203.01739

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