So far, we have covered 26 entries of Ramanujan. Talk 5 in the series Ramanujan Explained contains background material on infinite products. The idea in this is to cover some of the background material on infinite products so we can take limits of ratios of some infinite products and obtain hypergeometric special cases. This will help us rapidly increase the count of Ramanujan’s entries, and also help set us up for entries involving theta functions.
Title: Ramanujan Explained 5: The q-Gamma function
Speaker: Gaurav Bhatnagar (Ashoka University)
When: Thursday, July 25, 2024, 4:00 PM- 5:00 PM IST
Where: Zoom: Write to the organisers (sfandnt at gmail dot com) for the link
Abstract
We introduce infinite products and learn how to formally take limits of some ratios of infinite products. This is regarding the $q$-gamma function. Ramanujan had mentioned this limit in Entry 1 of Chapter 16 (Entry III.16.1(ii)) so it is a basic tool in his armoury.
Ramanujan Explained 