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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

A full extension of the Rogers-Ramanujan continued fraction


Authors: George E. Andrews and Douglas Bowman
Journal: Proc. Amer. Math. Soc. 123 (1995), 3343-3350
MSC: Primary 33D15; Secondary 11B65, 33D80
MathSciNet review: 1277090
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Abstract: In this paper, we present the natural extension of the Rogers-Ramanujan continued fraction to the nonterminating very well-poised basic hypergeometric function $ _8{\phi _7}$. In a letter to Hardy, Ramanujan indicated that he possessed a four variable generalization. Our generalization has seven variables and is, perhaps, all one can expect from this method.


References [Enhancements On Off] (What's this?)

  • [1] George E. Andrews, On 𝑞-difference equations for certain well-poised basic hypergeometric series, Quart. J. Math. Oxford Ser. (2) 19 (1968), 433–447. MR 0237831 (38 #6112)
  • [2] George E. Andrews, On Rogers-Ramanujan type identities related to the modulus 11, Proc. London Math. Soc. (3) 30 (1975), 330–346. MR 0369247 (51 #5482)
  • [3] George E. Andrews, The theory of partitions, Addison-Wesley Publishing Co., Reading, Mass.-London-Amsterdam, 1976. Encyclopedia of Mathematics and its Applications, Vol. 2. MR 0557013 (58 #27738)
  • [4] W.N. Bailey, An identity involving Heine's basic hypergeometric series, J. London Math. Soc. 4 (1929), 254-257.
  • [5] George Gasper and Mizan Rahman, Basic hypergeometric series, Encyclopedia of Mathematics and its Applications, vol. 35, Cambridge University Press, Cambridge, 1990. With a foreword by Richard Askey. MR 1052153 (91d:33034)
  • [6] S. Ramanujan, Collected papers, Cambridge Univ. Press, Cambridge, 1927 (Reprinted: Chelsea, New York, 1962).
  • [7] G.N. Watson, A new proof of the Rogers-Ramanujan identities, J. London Math. Soc. 4 (1930), 4-9.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1995-1277090-8
PII: S 0002-9939(1995)1277090-8
Keywords: Rogers-Ramanujan, continued fractions
Article copyright: © Copyright 1995 American Mathematical Society