Error Bounds for Uniform Asymptotic Expansions-Modified Bessel Function of Purely Imaginary Order

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Original languageEnglish
Pages (from-to)759-780
Journal / PublicationChinese Annals of Mathematics. Series B
Issue number5
Publication statusPublished - 2010


The authors modify a method of Olde Daalhuis and Temme for representing the remainder and coefficients in Airy-type expansions of integrals. By using a class of rational functions, they express these quantities in terms of Cauchy-type integrals; these expressions are natural generalizations of integral representations of the coefficients and the remainders in the Taylor expansions of analytic functions. By using the new representation, a computable error bound for the remainder in the uniform asymptotic expansion of the modified Bessel function of purely imaginary order is derived. © 2010 Editorial Office of CAM (Fudan University) and Springer Berlin Heidelberg.

Research Area(s)

  • Airy function, Modified Bessel function of purely imaginary order, Uniform asymptotic expansion, Error bound