The Rogers-Ramanujan identities without Jacobi's triple product
The first bijective proof of the Rogers-Ramanujan identities was given in 1981 by \textit{A. M. Garsia} and \textit{S. C. Milne} [J. Comb. Theory, Ser. A 31, 289--339 (1981; Zbl 0477.05009)]. Subsequently another bijective proof was given by \textit{D. M. Bressoud} and \textit{D. Zeilberger} [Discrete Math. 38, 313--315 (1982; Zbl 0476.05010)]. Both of these proofs use an involution principle and Jacobi's triple product identity. The author here presents a proof which avoids the use of the Jacobi identity, instead making use of a finite rational function identity which converges to Jacobi's triple product in the limit.
scientific article; zbMATH DE number 4064995