ON PREECE'S IDENTITY AND OTHER CONTIGUOUS RESULTS

- Journal title : Communications of the Korean Mathematical Society
- Volume 20, Issue 1, 2005, pp.169-178
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/CKMS.2005.20.1.169

Title & Authors

ON PREECE'S IDENTITY AND OTHER CONTIGUOUS RESULTS

CHOI, JUNE-SANG; RATHIE ARJUN K.; BHOJAK BHARTI;

CHOI, JUNE-SANG; RATHIE ARJUN K.; BHOJAK BHARTI;

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

generalized hypergeometric series ;Dixon's summation formula for ;Whipple's summation theorem for a ;

Language

English

Cited by

References

1.

W. N. Bailey, Products of generalized hypergeometric series, Proc. London Math. Soc.(2) 28 (1928), 242-254

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

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