Mathematical Sciences

Lund University

  • Title: The Rogers-Ramanujan Identities and their Generalizations
  • Description: The Rogers-Ramanujan identities were fi rst discovered and proved by L.J. Rogers, and appear as corollaries to more general results in a paper published by him in 1894. They were later rediscovered and proved by both S. Ramanujan and I. Schur. In this paper we present three proofs to the Rogers-Ramanujan identities. The first two proofs are due to Rogers and Ramanujan and are both highly inspired by Rogers' work from 1894. The third one is due to Schur and it is a combinatorial proof. A generalization of the Rogers-Ramanujan identities for all moduli is also stated and proved. For this we use generalizations of the identities due to B. Gordon, G.E. Andrews and D.M. Bressoud. We end the paper with a short discussion regarding the theta function's involvement in the proofs of the mentioned identities.
  • Start Date: Sept. 18, 2011
  • Finished Date: Sept. 21, 2012
  • Supervisor: Arne Meurman
  • Student: Selma Logo
  • Report (338.6 KB)
  • Popular Science Report (144.8 KB)