Error Bounds for Uniform Asymptotic Expansions-Modified Bessel Function of Purely Imaginary Order
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.
作 者： Wei SHI Roderick WONG 作者单位： Wei SHI(Wuhan Institute of Physics and Mathematics, The Chinese Academy of Sciences, Wuhan 430071, China)Roderick WONG(Department of Mathematics, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong)
刊 名： 数学年刊B辑（英文版） ISTIC SCI 英文刊名： CHINESE ANNALS OF MATHEMATICS,SERIES B 年，卷(期)： 2010 31(5) 分类号： O1 关键词： Modified Bessel function of purely imaginary order Airy function Uniform asymptotic expansion Error bound