带有显式误差项的贝塞尔和艾里函数的近似

Q1 Mathematics

Lms Journal of Computation and Mathematics Pub Date : 2014-01-01 DOI:10.1112/S1461157013000351

I. Krasikov

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引用次数: 50

摘要

我们展示了如何从适当的上界开始，得到一些具有非常明确误差项的特殊函数的渐近表达式。我们将计算出贝塞尔函数Jν(x)和艾里函数Ai(x)的细节。特别地，我们回答了Olenko提出的一个问题，并找到了Jν(x)与它的标准渐近差的一个尖锐的界。我们也给出了零点Ai(x)的一个非常简单和精确的近似值。

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Approximations for the Bessel and Airy functions with an explicit error term

We show how one can obtain an asymptotic expression for some special functions with a very explicit error term starting from appropriate upper bounds. We will work out the details for the Bessel function Jν(x) and the Airy function Ai(x). In particular, we answer a question raised by Olenko and find a sharp bound on the difference between Jν(x) and its standard asymptotics. We also give a very simple and surprisingly precise approximation for the zeros Ai(x).

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来源期刊

Lms Journal of Computation and Mathematics MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.60

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： LMS Journal of Computation and Mathematics has ceased publication. Its final volume is Volume 20 (2017). LMS Journal of Computation and Mathematics is an electronic-only resource that comprises papers on the computational aspects of mathematics, mathematical aspects of computation, and papers in mathematics which benefit from having been published electronically. The journal is refereed to the same high standard as the established LMS journals, and carries a commitment from the LMS to keep it archived into the indefinite future. Access is free until further notice.