A note on generalizations of Bailey's identity involving products of generalized hypergeometric series
2
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
In the theory of hypergeometric and generalized hypergeometric series, the well-known and very useful identity due to Bailey (which is a generalization of the Preece's identity) plays an important role. The aim of this research paper is to provide generalizations of Bailey's identity involving products of generalized hypergeometric series in the most general form. A few known, as well as new results, have also been obtained as special cases of our main findings.
Abstract
In the theory of hypergeometric and generalized hypergeometric series, the well-known and very useful identity due to Bailey (which is a generalization of the Preece's identity) plays an important role. The aim of this research paper is to provide generalizations of Bailey's identity involving products of generalized hypergeometric series in the most general form. A few known, as well as new results, have also been obtained as special cases of our main findings.
참고문헌 (14)
- W. N. Bailey, "Products of Generalized Hypergeometric Series", Proceedings of the London Mathematical Society, s2-28(1), pp.242~254 (1928), Wiley[DOI]
- W. N. Bailey, "Generalized hypergeometric series" (1964), Stechert-Hafner, Inc
- YOUNG SUP KIM, "Applications of extended Watson's summation theorem", TURKISH JOURNAL OF MATHEMATICS, 42(2), pp.418~443 (2018), The Scientific and Technological Research Council of Turkey (TUBITAK-ULAKBIM) - DIGITAL COMMONS JOURNALS[DOI]
- Yong Sup Kim, "Extensions of certain classical sum-mation theorems for the series 2F1, 3F2, and 4F3 with applications in Ramanu-jan's summations", International Journal of Mathematics and Mathematical Sciences, 2010, pp.1~26 (2010), Hindawi Limited[DOI]
- I. Kim, "Note on the generalization of Bailey's identity and two contiguous results", Bull. Kerala Math. Assoc, 16(2), pp.1~11 (2019)
- C. T. Preece, "The Product of two Generalised Hypergeometric Functions", Proceedings of the London Mathematical Society, s2-22(1), pp.370~380 (1924), Wiley[DOI]
- A. P. Prudnikov, "Integrals and series. Vol. 3" (1990), Gordon and Breach Science Publishers
- E. D. Rainville, "Special Functions" (1960), The Macmillan Co
- Medhat A. Rakha, "Generalizations of classical summation theorems for the series 2F1 and 3F2 with applications", Integral Transforms and Special Functions, 22(11), pp.823~840 (2011), Informa UK Limited[DOI]
- A. K. Rathie, "A short proof of Preece's identities and other contiguous results", Rev. Mat. Estatíst, 15, pp.207~210 (1997)
- A. K. Rathie, "Another proof of Kummer's second theorem", Commun. Korean Math. Soc, 13(4), pp.933~936 (1998)
- A. K. Rathie, "A note on generalizations of Preece's identity and other contiguous results", Bull. Korean Math. Soc, 35(2), pp.339~344 (1998)
- A. K. Rathie, "On Kummer's second theorem involving product of gener-alized hypergeometric series", Matematiche(Catania), 50(1), pp.35~38 (1995)
- A. K. Rathie, "New summation formula for 3F2(12)and a Kummer-type II transformation of 2F2(x)", Math. Commun, 13(1), pp.63~66 (2008)
