超几何函数、合流超几何函数和WKB解

Pub Date : 2021-01-01 DOI:10.2969/jmsj/84528452

T. Aoki, Toshinori Takahashi, M. Tanda

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引用次数: 2

摘要

建立了大参数超几何函数与大参数超几何微分方程WKB解的Borel和之间的关系。从精确WKB分析的角度研究了合流超几何函数。作为应用，得到了这些经典特殊函数关于参数的渐近展开式。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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The hypergeometric function, the confluent hypergeometric function and WKB solutions

Relations between the hypergeometric function with a large parameter and Borel sums of WKB solutions of the hypergeometric differential equation with the large parameter are established. The confluent hypergeometric function is also investigated from the viewpoint of exact WKB analysis. As applications, asymptotic expansion formulas for those classical special functions with respect to parameters are obtained.

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