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| Error Bounds for Uniform Asymptotic Expansions—Modified Bessel Function of Purely Imaginary Order |
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Citation： |
Wei SHI,Roderick WONG.Error Bounds for Uniform Asymptotic Expansions—Modified Bessel Function of Purely Imaginary Order[J].Chinese Annals of Mathematics B,2010,31(5):759~780 |
| Page view： 2109
Net amount： 1544 |
Authors： |
Wei SHI; Roderick WONG; |
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| Abstract： |
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. |
Keywords： |
Modified Bessel function of purely imaginary order, Airy function,
Uniform asymptotic expansion, Error bound |
Classification： |
41A60, 33E20, 30E20 |
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