ON PARTITIONS, ORTHOGONAL POLYNOMIALS AND THE EXPANSION OF CERTAIN INFINITE PRODUCTS By D. M. BRESSOUDj [Received 2 July 1979] "... Rogers (was) a mathematician of great talent but comparatively little reputation, now remembered mainly from Ramanujan's rediscovery of his work. Rogers was a fine analyst, whose gifts were, on a smaller scale, not unlike Ramanujan's; but no one paid much attention to anything he did . . . " G. H. Hardy in Ramanuj'an The results of Rogers which Ramanujan (and also I. J. Schur) independently rediscovered are (o.i) ri ( n^O, ±2(mod5) and (0.2) n n do i+J !, 2 • nmO. ±l(mod5) v v/v 1 / \ 1 ' These are the Rogers-Ramanujan identities and are best known for their combinatorial interpretation (due, independently, to MacMahon and Schur): (0.3) the partitions of an integer into parts congruent to ± 1, mod 5, are equinumerous with the partitions of that integer into parts with minimal difference 2; (0.4) the partitions of an integer into parts congruent to + 2, mod 5, are equinumerous with the partitions of that integer into parts with minimal difference 2 and smallest part at least 2. Even after the Rogers-Ramanujan identities were brought to the attention of the mathematical community by Hardy, little notice was t Partially supported by National Science Foundation Grant MCS 77-22992. Proc. London Math. Soc. (3) 42 (1981) 478-500