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http://dx.doi.org/10.4134/CKMS.2005.20.2.395

THREE-TERM CONTIGUOUS FUNCTIONAL RELATIONS FOR BASIC HYPERGEOMETRIC SERIES ₂φ₁

KIM, YONG-SUP (Department of Mathematics Wonkwang University)
RATHIE ARJUN K. (Department of Mathematics Govt. Dungar College(Bikaner University))
CHOI, JUNE-SANG (Department of Mathematics College of Natural Sciences Dongguk University)

Publication Information

Communications of the Korean Mathematical Society / v.20, no.2, 2005 , pp. 395-403 More about this Journal

Abstract

The authors aim mainly at giving fifteen three-term contiguous relations for the basic hypergeometric series $series\;_2{\phi}_1$ corresponding to Gauss's contiguous relations for the hypergeometric series $series\;_2F_1$ given in Rainville([6], p.71). They also apply them to obtain two summation formulas closely related to a known q-analogue of Kummer's theorem.

Keywords

basic hypergeometric series; q-analogue of Kummer's summation theorem; Gauss's summation theorem; Gauss's contiguous relations;

Citations & Related Records

Times Cited By KSCI : 1 (Citation Analysis)

Reference
Cited By KSCI

1	E. D. Rainville, Special Funtions, Macmillan Company, New York, 1960
2	A. K. Rathie and Y. S. Kim, On a q-analog of Kummer's theorem and its contiguous results, Comm. Korean Math. Soc. 18 (2003), no. 1, 151-157 DOI ScienceOn
3	G. E. Andrews, On the q-analog of Kummer's theorem and application, Duke Math. J. 40 (1973), no. 3, 525-528 DOI
4	W. N. Bailey, A note on a certain q-identities, Quart. J. Mech. Appl. Math. 12(1941), 173-175
5	J. A. Daum, The basic analog of Kummer's theorem, Bull. Amer. Math. Soc. 48 (1942), 711-713 DOI
6	G. Gasper and H. Rahman, Basic Hypergeometric Series, Cambridge University Press, 1990
7	E. Heine, Unterschungen uber die Reihe ..., J. Reine Angew. Math. 34 (1847), 285-328

KSCI

THREE-TERM CONTIGUOUS FUNCTIONAL RELATIONS FOR BASIC HYPERGEOMETRIC SERIES 2φ1

THREE-TERM CONTIGUOUS FUNCTIONAL RELATIONS FOR BASIC HYPERGEOMETRIC SERIES ₂φ₁