The Bailey Lattice

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.