Andrews

There are two absolutely fascinating formulas in Ramanujan's Lost Notebook that will form the subject of this presentation. One of these formulas provides an infinite product representation for the two variable Rogers-Ramanujan series and the other provides a comparable product for the partial theta series. In this talk I shall attempt to provide a comprehensible account of how the proofs of these results were obtained. On the surface each relies on the theory of entire functions and Hadamard's famous product representation of entire functions. However, much more detailed information is required for a complete understanding of Ramanujan's discoveries. The road to enlightenment starts with the Stieltjes-Wigert polynomials and an old paper of Szegö. Very recently W. Hayman has developed quite different techniques that also establish part of Ramanujan's results.