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Continued fraction formulae involving ratios of three gamma functions

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arxiv 2111.14143 v1 pith:SGV5KNTP submitted 2021-11-28 math.NT

Xiaodong Cao , Yoshio Tanigawa , Wenguang Zhai This is my paper · ORCID
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keywords threebauer-muircontinuedfiveformulaefractionfunctionsgamma
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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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  1. Continued Fractions of Polynomial Type: Theory and Encyclopedic Dictionary

    math.NT 2026-07 conditional novelty 6.5 of 10

    A theory-plus-dictionary of polynomial-type continued fractions with explicit convergence rates and Apéry-style accelerations, mostly new or newly quantified.

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