Hostname: page-component-7bb8b95d7b-s9k8s Total loading time: 0 Render date: 2024-09-11T08:00:38.473Z Has data issue: false hasContentIssue false

Sur Une Formule de Ramanujan-Bailey

Published online by Cambridge University Press:  20 November 2018

Jiang Zeng*
Affiliation:
Département de mathématique, Université Louis-Pasteur, 7, rue René-Descartes, F-67084 Strausbourg, France
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The Ramanujan-Bailey identity that establishes a symmetric relation between two hypergeometric series 3F2 is extended to a symmetric relation between two hypergeometric series 4F3. We also give a symmetric model that makes this symmetry evident.

Résumé

Résumé

L'identité de Ramanujan-Bailey, qui établit une relation symétrique entre deux séries hypergéométriques 3F2, est généralisée en une relation symétrique entre deux séries hypergéométriques 4F3. On construit également un modèle symétrique qui rend compte de cette symétrie.

Keywords

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1990

References

1. Al-Salam, W.A. and Fields, J.L., An identity for Double Hypergeometric Series, (Problem 85-24 proposed by Srivastava (H.M.), SIAM Review, v. 28 (1986), p. 576578.Google Scholar
2. Bailey, W., The partial sum of the coefficients of the hyper geometric series, J. London Math. Soc, v. 6 (1931), p. 4041.Google Scholar
3. Bailey, W., On one of Ramanujans theorems, J. London Math. Soc, v. 7 (1932), p. 3436.Google Scholar
4. Bailey, W., Generalized hyper geometric series. Cambridge, The University Press, (1935).Google Scholar
5. Darling, H.B.C., On a proof of one of Ramanujan s theorems, J. London Math. Soc, v. 5 (1930), p. 89.Google Scholar
6. Foata, Dominique and Strehl, Volker , Combinatorics ofLaguerre polynomials, Enumeration and Design [Waterloo. June-July 1982: Jackson, D.M. and Vanstone, S.A., eds.], p. 123140. (Toronto, Academic Press, 1984).Google Scholar
7. Hardy, G.H., Ramanujan (New York, Chelsea, 1940).Google Scholar
8. Hodgkinson, J., Note on one of Ramanujan's theorems, J. London Math. Soc, v. 6 (1931), p. 42–3.Google Scholar
9. Jackson, F.H., On q-definite integrals, Quart. J. Pure and Appl. Math., v. 41 (1910), p. 193203.Google Scholar
10. Joichi, J.T. and Dennis Stanton, Bijective proofs of basic hyper geometric series identities, Pacific J. Math., v. 127 (1987), p. 103120.Google Scholar
11. Ramanujan, Srinivasa, Collected Papers (New York, Chelsea, reprinted in 1962).Google Scholar
12. Slater, Lucy Joan, Generalized hyper geometric functions (Cambridge, The University Press, 1966).Google Scholar
13. Watson, G.N., Theorems stated by Ramanujan (VIII):, Theorems on divergent series, J. London Math. Soc, v. 4 (1929), p. 8286.Google Scholar
14. Watson, G.N., The constants of Landau and Lebesgue, Quarterly J. Math., v. I (1930), p. 310318.Google Scholar
15. Whipple, F.J.W., The sum of the coefficients of a hyper geometric series, J. London Math. Soc, v. 5 (1930), p. 192.Google Scholar
16. Wimp, Jet, Explicit formulas for the associated Jacobi polynomials and some applications, Can. J. Math., v. 34 (1987), p. 9831000.Google Scholar
17. Zeng, Jiang, Un modèle symétrique pour l'identité de Al-Salam-Fields, à paraître dans Discrete Math.Google Scholar