We revisit the umbral methods used by L. J. Rogers in his second proof of the Rogers-Ramanujan identities. We shall study how subsequent methods such as the Bailey chains and their variants arise naturally from Rogers' insights. We conclude with the introduction of multi-dimensional Bailey chains and apply them to prove some new Pentagonal Number Theorems.
All Science Journal Classification (ASJC) codes
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics