An analogy of Jacobi's formula and its applications
Classical Analysis and ODEs
2022-02-25 v1 Algebraic Geometry
Abstract
We give an analogy of Jacobi's formula, which relates the hypergeometric function with parameters 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.
Keywords
Cite
@article{arxiv.2202.11856,
title = {An analogy of Jacobi's formula and its applications},
author = {Jun Chiba and Keiji Matsumoto},
journal= {arXiv preprint arXiv:2202.11856},
year = {2022}
}
Comments
21 pages, 1 figure