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.
Funding Statement
The first author is supported by JSPS KAKENHI Grant Nos. 26400126 and 18K03385. The third author is supported by JSPS KAKENHI Grant No. 18K13433.
Citation
Takashi AOKI. Toshinori TAKAHASHI. Mika TANDA. "The hypergeometric function, the confluent hypergeometric function and WKB solutions." J. Math. Soc. Japan 73 (4) 1019 - 1062, October, 2021. https://doi.org/10.2969/jmsj/84528452
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