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Authors
Affiliations
1 Pennsylvania State University, Mont Alto, US
2 Pennsylvania State University, University Park, US
Source
The Journal of the Indian Mathematical Society, Vol 51, No 1-2 (1987), Pagination: 57-73
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.
