Indefinite q-integrals of quotients of q-hypergeometric functions

Heragy, Gamela E.; Mansour, Zeinab S. I.; Oraby, Karima

doi:10.21608/fsrt.2023.201930.1089

	Indefinite q-integrals of quotients of q-hypergeometric functions
Frontiers in Scientific Research and Technology
Volume 6, Issue 1, August 2023 PDF (1.33 MB)
Document Type: Original Article
DOI: 10.21608/fsrt.2023.201930.1089
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Authors
Gamela E. Heragy¹; Zeinab S. I. Mansour²; Karima Oraby ¹
¹Suez University
²Cairo University
Abstract
This paper uses Heine contiguous relations for the basic hypergeometric function ${}_2\phi_1$, the $q$-integrating factor method for solving linear first order $q$-difference equations, and an indefinite $q$-integral formula involving two arbitrary functions to derive indefinite $q$-integrals involving quotients of the hypergeometric functions ${}_2\phi_1$. This paper uses Heine contiguous relations for the basic hypergeometric function ${}_2\phi_1$, the $q$-integrating factor method for solving linear first order $q$-difference equations, and an indefinite $q$-integral formula involving two arbitrary functions to derive indefinite $q$-integrals involving quotients of the hypergeometric functions ${}_2\phi_1$.This paper uses Heine contiguous relations for the basic hypergeometric function ${}_2\phi_1$, the $q$-integrating factor method for solving linear first order $q$-difference equations, and an indefinite $q$-integral formula involving two arbitrary functions to derive indefinite $q$-integrals involving quotients of the hypergeometric functions ${}_2\phi_1$.This paper uses Heine contiguous relations for the basic hypergeometric function ${}_2\phi_1$, the $q$-integrating factor method for solving linear first order $q$-difference equations, and an indefinite $q$-integral formula involving two arbitrary functions to derive indefinite $q$-integrals involving quotients of the hypergeometric functions ${}_2\phi_1$.
Keywords
Jackson's $q$-integrals; $q$-hypergeometric function; Heine $q$-contiguous relations


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