The Bailey Lattice

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Authors

  • Pennsylvania State University, Mont Alto ,US
  • Pennsylvania State University, University Park ,US
  • Pennsylvania State University, University Park ,US

Abstract

The Rogers-Ramanujan identities [5; ch. 7] are given analytically by the following formulae: (|q|<1)
1+∑qn2/(1-q)(1-q2)...(1-qn) (1.1)
=∑1/(1-q5n+1)(1-q5n+2)2
1+∑qn2+n/(1-q)(1-q2)...(1-qn) (1.2)
=∑1/(1-q5n+2)(1-q5n+3)
These are equivalent respectively to the following combinatorial identities:
The number of partitions of n into parts with difference at least 2 equals the number of partitions of n into parts congruent to ±1, modulo 5.

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Published

1987-06-01

How to Cite

Agarwal, A. K., Andrews, G. E., & Bressoud, D. M. (1987). The Bailey Lattice. The Journal of the Indian Mathematical Society, 51(1-2), 57–73. Retrieved from https://informaticsjournals.com/index.php/jims/article/view/22020