Heine's method and $A_n$ to $A_m$ transformation formulas
Classical Analysis and ODEs
2019-05-01 v2
Abstract
We apply Heine's method---the key idea Heine used in 1846 to derive his famous transformation formula for series---to multiple basic series over the root system of type . In the classical case, this leads to a bibasic extension of Heine's formula, which was implicit in a paper of Andrews which he wrote in 1966. As special cases, we recover extensions of many of Ramanujan's transformations. In addition, we extend previous work of the author regarding a bibasic extension of Andrews' -Lauricella function, and show how to obtain very general transformation formulas of this type. The results obtained include transformations of an -fold sum into an -fold sum.
Cite
@article{arxiv.1705.10095,
title = {Heine's method and $A_n$ to $A_m$ transformation formulas},
author = {Gaurav Bhatnagar},
journal= {arXiv preprint arXiv:1705.10095},
year = {2019}
}
Comments
23 pages (Accepted in Ramanujan J.)