Macdonald函数的上界和渐近展开式及Kontorovich-Ledev积分的可和性

IF 0.7 3区数学 Q2 MATHEMATICS

Integral Transforms and Special Functions Pub Date : 2022-11-07 DOI:10.1080/10652469.2023.2190590

S. Yakubovich

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引用次数: 0

摘要

建立了Macdonald函数的一致上界和具有显式余项的渐近展开式。这些结果可以应用于研究Jones意义下的发散Kontorovich-Lebedev积分的可和性。也就是说，我们肯定地回答了一个问题（参见[Ehrenmark U.用一类发散逆Kontorovich Lebedev变换进行的可和性实验。Comput Math Appl.2018；76（1）:141–154.]），这些积分是否在弱意义上收敛于甚至整个指数型函数。

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Upper bounds and asymptotic expansion for Macdonald's function and the summability of the Kontorovich-Lebedev integrals

Uniform upper bounds and the asymptotic expansion with an explicit remainder term are established for the Macdonald function . The results can be applied, for instance, to study the summability of the divergent Kontorovich-Lebedev integrals in the sense of Jones. Namely, we answer affirmatively a question (cf. [Ehrenmark U. Summability experiments with a class of divergent inverse Kontorovich-Lebedev transforms. Comput Math Appl. 2018;76(1):141–154.]) whether these integrals converge for even entire functions of the exponential type in a weak sense.

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来源期刊

Integral Transforms and Special Functions 数学-数学

CiteScore

2.20

自引率

20.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Integral Transforms and Special Functions belongs to the basic subjects of mathematical analysis, the theory of differential and integral equations, approximation theory, and to many other areas of pure and applied mathematics. Although centuries old, these subjects are under intense development, for use in pure and applied mathematics, physics, engineering and computer science. This stimulates continuous interest for researchers in these fields. The aim of Integral Transforms and Special Functions is to foster further growth by providing a means for the publication of important research on all aspects of the subjects.