Geodesic
Further Results on Multiple $q$-Eulerian Integrals for Various $Q$-Hypergeometric Functions
Publications de l'Institut Mathématique, _N_S_108 (2020) no. 122, p. 63

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We continue the study of single and multiple $q$-Eulerian integrals in the spirit of Exton, Driver, Johnston, Pandey, Saran and Erdélyi. The method of proof is often the $q$-beta integral method with the correct $q$-power together with the $q$-binomial theorem. By the Totov method we can prove summation theorems as special cases of multiple $q$-Eulerian integrals. The Srivastava $\triangle$ notation for $q$-hypergeometric functions is used to enable the shortest possible form of the long formulas. The various $q$-Eulerian integrals are in fact meromorphic continuations of the various multiple $q$-functions, suitable for numerical computations. In the end of the paper a generalization of the $q$-binomial theorem is used to find $q$-analogues of a multiple integral formulas for $q$-Kampé de Fériet functions.
DOI : 10.2298/PIM2022063E
Classification : 33D60, 33D15 33C65 
Thomas Ernst. Further Results on Multiple $q$-Eulerian Integrals for Various $Q$-Hypergeometric Functions. Publications de l'Institut Mathématique, _N_S_108 (2020) no. 122, p. 63 . doi: 10.2298/PIM2022063E
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