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2021•Journal of the Mathematical Society of JapanRequires access

The hypergeometric function, the confluent hypergeometric function and WKB solutions

Takashi Aoki, Toshinori Takahashi, Mika Tanda

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Abstract

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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What this paper is about

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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OpenAlex reports 6 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

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.

Key concepts: Confluent hypergeometric function, Generalized hypergeometric function, Hypergeometric function of a matrix argument, Mathematics, WKB approximation, Basic hypergeometric series, Hypergeometric function, Hypergeometric identity

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