DOI QR코드

DOI QR Code

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)
  • Published : 2005.04.01

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.

References

  1. G. E. Andrews, On the q-analog of Kummer's theorem and application, Duke Math. J. 40 (1973), no. 3, 525-528 https://doi.org/10.1215/S0012-7094-73-04045-3
  2. W. N. Bailey, A note on a certain q-identities, Quart. J. Mech. Appl. Math. 12(1941), 173-175
  3. J. A. Daum, The basic analog of Kummer's theorem, Bull. Amer. Math. Soc. 48 (1942), 711-713 https://doi.org/10.1090/S0002-9904-1942-07764-0
  4. G. Gasper and H. Rahman, Basic Hypergeometric Series, Cambridge University Press, 1990
  5. E. Heine, Unterschungen uber die Reihe ..., J. Reine Angew. Math. 34 (1847), 285-328
  6. E. D. Rainville, Special Funtions, Macmillan Company, New York, 1960
  7. 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 https://doi.org/10.4134/CKMS.2003.18.1.151

Cited by

  1. A STUDY OF Q-CONTIGUOUS FUNCTION RELATIONS vol.31, pp.1, 2016, https://doi.org/10.4134/CKMS.2016.31.1.065