A Determinant Identity that Implies Rogers-Ramanujan

One-parameter Generalizations of Rogers-Ramanujan Type Identities

Resorting to the recursions satisfied by the polynomials which converge to the right hand sides of the Rogers-Ramanujan type identities given by Sills [17] and determinant method presented in [9], we obtain many new one-parameter generalizations of the Rogers-Ramanujan type identities, such as a generalization of the analytic versions of the first and second Göllnitz-Gordon partition identities...

AN ELLIPTIC BCn BAILEY LEMMA, MULTIPLE ROGERS–RAMANUJAN IDENTITIES AND EULER’S PENTAGONAL NUMBER THEOREMS

An elliptic BCn generalization of the classical two parameter Bailey Lemma is proved, and a basic one parameter BCn Bailey Lemma is obtained as a limiting case. Several summation and transformation formulas associated with the root system BCn are proved as applications, including a 6φ5 summation formula, a generalized Watson transformation and an unspecialized Rogers–Selberg identity. The last ...

Proofs of the Rogers - RamanujanIdentities and of Identities of Similar

New short and easy computer proofs of nite versions of the Rogers-Ramanujan identities and of similar type are given. These include a very short proof of the rst Rogers-Ramanujan identity that was missed by computers, and a new proof of the well-known quintuple product identity by creative telescoping.

Math 7012 Enumerative Combinatorics Project: Introduction to a combinatorial proof of the Rogers-Ramanujan and Schur identities and an application of Rogers-Ramanujan identity

Easy Computer Proofs of the Rogers - RamanujanIdentities and of Identities of Similar

New short and easy computer proofs of nite versions of the Rogers-Ramanujan identities and of similar type are given. These include a very short proof of the rst Rogers-Ramanujan identity that was missed by computers, and a new proof of the well-known quintuple product identity by creative telescoping.