The Rogers-Ramanujan identities have reached the ripe-old age of one hundred and five and are still the subject of active research. We will discuss their fascinating history, some of the number theory and combinatorics they encapture, and what they have to do with the 1998 Nobel Prize in physics. 1. The Rogers–Ramanujan identities In this lecture you will be introduced to the Rogers–Ramanujan i...

The Bailey lemma is a famous tool to prove Rogers-Ramanujan type identities. We use shifted versions of the Bailey lemma to derive mversions of multisum Rogers-Ramanujan type identities. We also apply this method to the Well-Poised Bailey lemma and obtain a new extension of the Rogers-Ramanujan identities.

We obtain Mehler’s formula and the Rogers formula for the continuous big qHermite polynomials Hn(x; a|q). Instead of working with the polynomials Hn(x; a|q) directly, we consider the equivalent forms in terms of the bivariate Rogers-Szegö polynomials hn(x, y|q) recently introduced by Chen, Fu and Zhang. It turns out that Mehler’s formula for Hn(x; a|q) involves a 3φ2 sum, and the Rogers formula...

Recently we interpreted five q-series identities of Rogers combinatorially by using partitions with “n + t copies of n” of Agarwal and Andrews [1]. In this paper we use lattice paths of Agarwal and Bressoud [2] to provide new combinatorial interpretations of the same identities. This results in five new 3-way combinatorial identities.

Ramanujan’s lost notebook contains several identities arising from the Rogers–Fine identity and/or Rogers’ false theta functions. Combinatorial proofs for many of these identities are given.

N ature is full of curves. So it is only natural that manmade devices meant to interact with nature emulate its elements of design. That is the line of reasoning behind the innovations of John Rogers, a member of the National Academy of Engineering and a professor of materials science at the University of Illinois, Urbana-Champaign. Rogers’ innovations have inspired an array of approaches to re...

and management. Br Med J 2:157-161, 1970 3 Kumura, Falke K, Geffin B, et al: Continuous positive pressure ventilation in acute respiratory failure. N Engl J Med 283:1430-1436, 1970 4 Rutledge RR, Flor RJ: The use of mechanical ventilation with positive end expiratory pressure in the treatment of near-drowning. Anesthesiology 38:194-196, 1973 5 Petty T, Ashbaugh D: The adult respiratory distress...