A note on the asymptotics of the modified Bessel functions on the Stokes lines

R. B. Paris

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    Abstract

    We employ the exponentially improved asymptotic expansions of the confluent hypergeometric functions on the Stokes lines discussed by the author [Appl. Math. Sci. 7 (2013) 6601–6609] to give the analogous expansions of the modified Bessel functions Iν(z) and Kν(z) for large z and finite ν on arg z = ±π (and, in the case of Iν(z), also on arg z = 0). Numerical results are presented to illustrate the accuracy of these expansions.
    Original languageEnglish
    Pages (from-to)407-416
    Number of pages10
    JournalMathematica Æterna
    Volume7
    Issue number4
    Publication statusPublished - 2017

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