The hypergeometric function, the confluent hypergeometric function and WKB solutions
- 22 October 2021
- journal article
- research article
- Published by Mathematical Society of Japan (Project Euclid) in Journal of the Mathematical Society of Japan
- Vol. 73 (4), 1-44
- https://doi.org/10.2969/jmsj/84528452
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.Keywords
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