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

Error Bounds for Uniform Asymptotic Expansions-Modified Bessel Function of Purely Imaginary Order
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摘要 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 coe?cients 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. 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 coe？cients 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
机构地区 Wuhan Institute of Physics and Mathematics Department of Mathematics
出处 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2010年第5期759-780,共22页 数学年刊（B辑英文版）
关键词 渐近展开 误差界 虚函数 塞尔 高阶 积分计算 泰勒展开式 有理函数 Modified Bessel function of purely imaginary order,Airy function,Uniform asymptotic expansion,Error bound
分类号 O175.8 [理学—基础数学] O223 [理学—运筹学与控制论]
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参考文献16

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Chinese Annals of Mathematics,Series B
2010年 第5期

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