DOI QR코드

DOI QR Code

ON PREECE'S IDENTITY AND OTHER CONTIGUOUS RESULTS

  • CHOI, JUNE-SANG (Department of Mathematics College of Natural Sciences Dongguk University) ;
  • RATHIE ARJUN K. (Department of Mathematics Dungar College) ;
  • BHOJAK BHARTI (Department of Mathematics Dungar College)
  • Published : 2005.01.01

Abstract

Five results closely related to the well-known Preece's identity obtained earlier by Choi and Rathie will be derived here by using some known hypergeometric identities. In addition to this, the identities obtained earlier by Choi and Rathie have also been written in a compact form.

Keywords

References

  1. W. N. Bailey, Products of generalized hypergeometric series, Proc. London Math. Soc.(2) 28 (1928), 242-254 https://doi.org/10.1112/plms/s2-28.1.242
  2. Y. S. Kim and A. K. Rathie, A generalization of Preece's identity, Commun. Korean Math. Soc. 14 (1999), 217-222
  3. E. E. Kummer, Uber die hypergeometrische Reihe F(a; b; x), J. Reine Angew. Math. 15 (1836), 39-83
  4. J. L. Lavoie, F. Grondin, and A. K. Rathie, Generalizations of Watson's theorem on the sum of a $_3F_2$, Indian J. Math. 34 (1992), 23-32
  5. J. L. Lavoie, F. Grondin, A. K. Rathie, and K. Arora, Generalizations of Dixon's theorem on the sum of a $_3F_2$, Math. Comp. 49 (1987), 269-274 https://doi.org/10.2307/2008264
  6. C. T. Preece, The product of two generalized hypergeometric functions, Proc. London Math. Soc.(2) 24 (1924), 370-380
  7. E. D. Rainville, Special Functions, The Macmillan Company, New York, 1960
  8. A. K. Rathie, A short proof of Preece's identity and other contiguous results, Rev. Mat. Estatist.(Brazil) 15 (1997), 207-210
  9. A. K. Rathie and J. Choi, A note on an identity due to Preece, Far East J. Math. Sci. 6 (1998), 205-209
  10. A. K. Rathie, A note on generalizations of Preece's identity and other contiguous results, Bull. Korean Math. Soc. 35 (1998), 339-344
  11. A. K. Rathie and S. Sharma, On a generalization of Preece's identity, Acta Cienc. Indica Math. 105 (1999), 167-168

Cited by

  1. M. Jackson’s bilateral 3 H 3-series and extension with integer parameters vol.30, pp.2, 2013, https://doi.org/10.1007/s11139-012-9392-8