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

• Type: Article in International Scientific Journal
• Date: 2023

Authors

Yakubovich, SB (Author) FCUP

Journal

Title: Integral Transforms and Special Functions

Vol. 34

Pages: 721-736

ISSN: 1065-2469

Publisher: Taylor & Francis

Indexing

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Other information

Authenticus ID: P-00Y-6K1

DOI: 10.1080/10652469.2023.2190590

Abstract (EN): Uniform upper bounds and the asymptotic expansion with an explicit remainder term are established for the Macdonald function K-it(x). 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 diver-gent 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.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 16