超几何函数、合流超几何函数和WKB解

IF 0.7 4区数学 Q2 MATHEMATICS

Journal of the Mathematical Society of Japan 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。

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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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来源期刊

Journal of the Mathematical Society of Japan 数学-数学

CiteScore

1.40

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of the Mathematical Society of Japan (JMSJ) was founded in 1948 and is published quarterly by the Mathematical Society of Japan (MSJ). It covers a wide range of pure mathematics. To maintain high standards, research articles in the journal are selected by the editorial board with the aid of distinguished international referees. Electronic access to the articles is offered through Project Euclid and J-STAGE. We provide free access to back issues three years after publication (available also at Online Index).