Indefinite q-integrals of quotients of q-hypergeometric functions | ||
| Frontiers in Scientific Research and Technology | ||
| Volume 6, Issue 1, August 2023 PDF (1.33 M) | ||
| Document Type: Original Article | ||
| DOI: 10.21608/fsrt.2023.201930.1089 | ||
| 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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