A full extension of the Rogers-Ramanujan continued fraction
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- by George E. Andrews and Douglas Bowman PDF
- Proc. Amer. Math. Soc. 123 (1995), 3343-3350 Request permission
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
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- George E. Andrews, The theory of partitions, Encyclopedia of Mathematics and its Applications, Vol. 2, Addison-Wesley Publishing Co., Reading, Mass.-London-Amsterdam, 1976. MR 0557013 W.N. Bailey, An identity involving Heine’s basic hypergeometric series, J. London Math. Soc. 4 (1929), 254-257.
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Additional Information
- © Copyright 1995 American Mathematical Society
- 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