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arXiv · 2111.14143

Continued fraction formulae involving ratios of three gamma functions

Xiaodong Cao·Yoshio Tanigawa·Wenguang Zhai
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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.

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Xiaodong Cao, Yoshio Tanigawa, Wenguang Zhai. 2021-11-28. Continued fraction formulae involving ratios of three gamma functions. https://arxiv.org/abs/2111.14143

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