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.
Citation
Jun CHIBA. Keiji MATSUMOTO. "An analogy of Jacobi's formula and its applications." Hokkaido Math. J. 52 (3) 463 - 494, October 2023. https://doi.org/10.14492/hokmj/2021-572
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