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arXiv · 2202.11856

An analogy of Jacobi's formula and its applications

Jun Chiba·Keiji Matsumoto
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Abstract

We give an analogy of Jacobi's formula, which relates the hypergeometric function with parameters $(1/4,1/4,1)$ and theta constants. By using this analogy and twice formulas of theta constants, we obtain a transformation formula for this hypergeometric function. As its application, we express the limit of a pair of sequences defined by a mean iteration by this hypergeometric function.

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Jun Chiba, Keiji Matsumoto. 2022-02-24. An analogy of Jacobi's formula and its applications. https://arxiv.org/abs/2202.11856

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