Continued fraction formulae involving ratios of three gamma functions
Number Theory
2021-11-30 v1
Abstract
Via the MC-algorithm, in this paper we produce seven continued fraction formulae involving products and quotients of three gamma functions with three parameters, and another is an extension of Entry 34 in Chapter 12 of Ramanujan's second notebook. Five of them will be proved rigorously by the Bauer-Muir transformation. A crucial ingredient in the proofs of our five theorems is to employ the Bauer-Muir transformation twice with different nonlinear modifying factors.
Keywords
Cite
@article{arxiv.2111.14143,
title = {Continued fraction formulae involving ratios of three gamma functions},
author = {Xiaodong Cao and Yoshio Tanigawa and Wenguang Zhai},
journal= {arXiv preprint arXiv:2111.14143},
year = {2021}
}
Comments
32 pages. Comments and remarks are welcome!