<%@ Page Language="C#" MasterPageFile="~/Main.master" AutoEventWireup="true" Title="Volume11 Issue1" %>
More Semi-Finite Forms of Bilateral Basic Hypergeometric Series
Frédéric Jouhet
Université Lyon1, CNRS, UMR 5208 Institut Camille Jordan, Bâtiment du Doyen Jean Braconnier, 43, blvd du 11 novembre 1918, F-69622 Villeurbanne Cedex, France
jouhet@math.univ-lyon1.fr
Annals of Combinatorics 11 (1) p.47-57 March, 2007
AMS Subject Classification: 33D15
Abstract:
We prove some new semi-finite forms of bilateral basic hypergeometric series. One of them yields in a direct limit Bailey's celebrated 6ψ6 summation formula, answering a question recently raised by Chen and Fu.
Keywords: bilateral basic hypergeometric series, q-series, Bailey's 6ψ6 summation

References:

1. G.E. Andrews, Applications of basic hypergeometric functions, SIAM Rev. 16 (1974) 441- 484.

2. R. Askey, The very well poised 6ψ6. II, Proc. Amer. Math. Soc. 90 (1984) 575-579.

3. R. Askey and M.E.H. Ismail, The very well poised 6ψ6, Proc. Amer. Math. Soc. 77 (1979) 218-222.

4. W.N. Bailey, Series of hypergeometric type which are infinite in both directions, Quart. J. Math. 7 (1936) 105-115.

5. W.N. Bailey, On the basic bilateral hypergeometric series 2ψ2, Quart. J. Math. Oxford Ser. (2) 1 (1950) 194-198.

6. T.J.l'A. Bromwich, An Introduction to the Theory of Infinite Series, 2nd Ed., Macmillan, London, 1949.

7. A.-L. Cauchy, Mémoire sur les fonctions dont plusieurs valeurs sont liées entre elles par une équation linéaire, et sur diverses transformations de produits composés d'un nombre indéfini de facteurs, C. R. Acad. Sci. Paris 17 (1843) 523.

8. W.Y.C. Chen and A.M. Fu, Semi-finite forms of bilateral basic hypergeometric series, Proc. Amer. Math. Soc. 134 (2006) 1719-1725.

9. G. Gasper and M. Rahman, Basic Hypergeometric Series, 2nd Ed., Encyclopedia of Mathematics and its Applications 96, Cambridge University Press, Cambridge, 2004.

10. C.G.J. Jacobi, Fundamenta Nova Theoriae Functionum Ellipticarum, Sumptibus fratrum Bornträger, Regiomonti, 1829.

11. F. Jouhet and M. Schlosser, Another proof of Bailey's 6ψ6 summation, Aequationes Math. 70 (1-2) (2005) 43-50.

12. M. Schlosser, A simple proof of Bailey's very-well-poised 6ψ6 summation, Proc. Amer. Math. Soc. 130 (2002) 1113-1123.

13. M. Schlosser, Abel-Rothe type generalizations of Jacobi's triple product identity, In: Theory and Applications of Special Functions, M.E.H. Ismail and E. Koelink, Eds., Dev. Math. 13 (2005) 383-400.

14. L.J. Slater, Generalized Hypergeometric Functions, Cambridge University Press, Cambridge, 1966.

15. L.J. Slater and A. Lakin, Two proofs of the 6ψ6 summation theorem, Proc. Edinburgh Math. Soc. (2) 9 (1956) 116-121.