Indefinite q-integrals of quotients of q-hypergeometric functions

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 ${}_2\phi_1$.