The hypergeometric function, the confluent hypergeometric function and WKB solutions

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  • Aoki Takashi
    Department of Mathematics, Kindai University
  • Takahashi Toshinori
    Institute for Fundamental Sciences, Faculty of Science and Engineering, Setsunan University
  • Tanda Mika
    Department of Mathematical Sciences, Kwansei Gakuin University

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Abstract

<p>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.</p>

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