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Basic hypergeometric identities: An introductory revisiting through the Carlitz inversions

Basic hypergeometric identities: An introductory revisiting through the Carlitz inversions Abstract. By means of the Carlitz ^-analogue of Gould-Hsu inverse relations, a quick introduction to the basic hypergeometric formulae is presented in an elementary and direct way. As a unified treatment, several famous identities, e.g., the ^-analogues of the DougallDixon-Watson-Whipple formulas, are shown to be the dual versions of the ^-Saalschutz theorem. 1991 Mathematics Subject Classification: 05A30; 33A30. 0. Introduction Following the usual notation, the basic hypergeometric series with base q and variable z (where \q\ < l and \z\ < 1) is defined by (cf. e.g., [12]) with <7-shifted factorials (O.lb) (*; q)a = ft (l - xq)n = (x; q)J(xq"; ?),, k =0 and ) ( 01 1 (gt; q\(a2\ q\ ... (flr; q)n instead of factorial-fractions. Partially supported by Alexander von Humboldt Foundation (Germany) Italian Consiglio Nazionale Delle Ricerche (CNR) NSF (Chinese), Youth-Grant 1990-1033 ChuWenchang After sleeping many years in the mathematical world, the basic hypergermetric series woke up and has aroused new interest during the last decade for its wide applications to mathematics, physics and Computer science. But most relations about ^-series seem to be like monsters to the non-specialist outside the circle of special functions. This fact has stimulated the author to seek http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Forum Mathematicum de Gruyter

Basic hypergeometric identities: An introductory revisiting through the Carlitz inversions

Forum Mathematicum , Volume 7 (7) – Jan 1, 1995

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Publisher
de Gruyter
Copyright
Copyright © 2009 Walter de Gruyter
ISSN
0933-7741
eISSN
1435-5337
DOI
10.1515/form.1995.7.117
Publisher site
See Article on Publisher Site

Abstract

Abstract. By means of the Carlitz ^-analogue of Gould-Hsu inverse relations, a quick introduction to the basic hypergeometric formulae is presented in an elementary and direct way. As a unified treatment, several famous identities, e.g., the ^-analogues of the DougallDixon-Watson-Whipple formulas, are shown to be the dual versions of the ^-Saalschutz theorem. 1991 Mathematics Subject Classification: 05A30; 33A30. 0. Introduction Following the usual notation, the basic hypergeometric series with base q and variable z (where \q\ < l and \z\ < 1) is defined by (cf. e.g., [12]) with <7-shifted factorials (O.lb) (*; q)a = ft (l - xq)n = (x; q)J(xq"; ?),, k =0 and ) ( 01 1 (gt; q\(a2\ q\ ... (flr; q)n instead of factorial-fractions. Partially supported by Alexander von Humboldt Foundation (Germany) Italian Consiglio Nazionale Delle Ricerche (CNR) NSF (Chinese), Youth-Grant 1990-1033 ChuWenchang After sleeping many years in the mathematical world, the basic hypergermetric series woke up and has aroused new interest during the last decade for its wide applications to mathematics, physics and Computer science. But most relations about ^-series seem to be like monsters to the non-specialist outside the circle of special functions. This fact has stimulated the author to seek

Journal

Forum Mathematicumde Gruyter

Published: Jan 1, 1995

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