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arXiv · 2205.04867

A Lagrangian method for indefinite q-integrals

Gamela E. Heragy·Zeinab S. I. Mansour·Karima M. Orabya
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Abstract

A Lagrangian method is introduced recently for deriving indefinite integrals of special functions that satisfy homogeneous (nonhomogeneous) second-order linear differential equations. This paper extends this method to include indefinite Jackson $q$-integrals of special functions satisfying homogeneous (nonhomogeneous) second-order linear $q$-difference equations. Many $q$-integrals, both previously known and completely new, are derived using the method. We introduce samples of indefinite and definite $q$-integrals for Jackson's $q$-Bessel functions, $q$-hypergeometric functions, and some orthogonal polynomials.

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BibTeXRIS

Gamela E. Heragy, Zeinab S. I. Mansour, Karima M. Orabya. 2022-05-10. A Lagrangian method for indefinite q-integrals. https://arxiv.org/abs/2205.04867

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