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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
DOI: https://doi.org/10.1090/S0002-9939-1995-1277090-8
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] G.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] -, On Rogers-Ramanujan type identities related to the modulus 11, Proc. London Math. Soc. (3) 30 (1975), 330-346. MR 0369247 (51:5482)
  • [3] -, The theory of partitions, Encyclopedia Math. Appl., vol. 2 (G.-C. Rota ed.), Addison-Wesley, Reading, 1976 (Reprinted: Cambridge Univ. Press, Cambridge, 1985). 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] G. Gasper and M. Rahman, Basic hypergeometric series, Encyclopedia Math. Appl., vol. 35 (G.-C. Rota ed.), Cambridge University Press, Cambridge, 1990. 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: https://doi.org/10.1090/S0002-9939-1995-1277090-8
Keywords: Rogers-Ramanujan, continued fractions
Article copyright: © Copyright 1995 American Mathematical Society

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