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Open AccessArticle

Convergence Aspects for Generalizations of q-Hypergeometric Functions

Department of Mathematics, Uppsala University, P.O. Box 480, SE-751 06 Uppsala, Sweden
Academic Editor: Florin Nichita
Axioms 2015, 4(2), 134-155;
Received: 6 September 2014 / Revised: 8 March 2015 / Accepted: 31 March 2015 / Published: 8 April 2015
(This article belongs to the Special Issue Hopf Algebras, Quantum Groups and Yang-Baxter Equations 2014)
PDF [259 KB, uploaded 8 April 2015]


In an earlier paper, we found transformation and summation formulas for 43 q-hypergeometric functions of 2n variables. The aim of the present article is to find convergence regions and a few conjectures of convergence regions for these functions based on a vector version of the Nova q-addition. These convergence regions are given in a purely formal way, extending the results of Karlsson (1976). The Γq-function and the q-binomial coefficients, which are used in the proofs, are adjusted accordingly. Furthermore, limits and special cases for the new functions, e.g., q-Lauricella functions and q-Horn functions, are pointed out. View Full-Text
Keywords: q-Stirling formula; even number of variables; Nova q-addition; inequality q-Stirling formula; even number of variables; Nova q-addition; inequality
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

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Ernst, T. Convergence Aspects for Generalizations of q-Hypergeometric Functions. Axioms 2015, 4, 134-155.

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