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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; https://doi.org/10.3390/axioms4020134
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)
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
MDPI and ACS Style

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

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