Further results on multiple q-Eulerian integrals for various q-hypergeometric functions | Zendy

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Further results on multiple q-Eulerian integrals for various q-hypergeometric functions

Author(s) -

Thomas Ernst

Publication year - 2020

Publication title -

publications de l institut mathematique

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.246

H-Index - 17

eISSN - 1820-7405

pISSN - 0350-1302

DOI - 10.2298/pim2022063e

Subject(s) - eulerian path , mathematics , hypergeometric function , generalization , binomial theorem , meromorphic function , pure mathematics , computation , multiple integral , discrete mathematics , algebra over a field , mathematical analysis , algorithm , lagrangian

We continue the study of single and multiple q-Eulerian integrals in the spirit of Exton, Driver, Johnston, Pandey, Saran and Erd?lyi. 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 ? 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-Kamp? de F?riet functions.

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