Home On an alternative to Wong’s asymptotic expansion of the Kontorovich–Lebedev transform near the origin
Article
Licensed
Unlicensed Requires Authentication

On an alternative to Wong’s asymptotic expansion of the Kontorovich–Lebedev transform near the origin

  • Derek Naylor EMAIL logo
Published/Copyright: February 15, 2019

Abstract

An asymptotic expansion is constructed for values near the origin of a function whose Kontorovich–Lebedev transform is an even analytic function. The expansion obtained is expressed in terms of the poles and residues of the analytic function and provides an alternative to one obtained by Wong (1981) which becomes inapplicable.

MSC 2010: 41A60; 44A15; 33C10

References

[1] N. Bleistein and R. A. Handelsman, Asymptotic Expansions of Integrals, Holt, Rinehart and Winston, New York, 1975. Search in Google Scholar

[2] G. Doetsch, Handbuch der Laplace-Transformation. Band 1, Birkhäuser, Basel, 1955. 10.1007/978-3-0348-4147-4Search in Google Scholar

[3] W. Magnus, F. Oberhettinger and R. P. Soni, Formulas and Theorems for the Special Functions of Mathematical Physics, Springer, New York, 1966. 10.1007/978-3-662-11761-3Search in Google Scholar

[4] J. P. McClure and R. Wong, Explicit error terms for asymptotic expansion of Stieltjes transforms, J. Inst. Math. Appl. 22 (1978), 129–145. 10.1093/imamat/22.2.129Search in Google Scholar

[5] D. Naylor, On an asymptotic expansion of the inverse Kontorovich–Lebedev transform, Analysis 24 (2004), 329–344. 10.1524/anly.2004.24.14.329Search in Google Scholar

[6] R. Wong, Asymptotic expansions of the Kontorovich–Lebedev transform, Appl. Anal. 12 (1981), 161–172. 10.1080/00036818108839358Search in Google Scholar

Received: 2018-07-25
Revised: 2018-11-28
Accepted: 2019-01-23
Published Online: 2019-02-15
Published in Print: 2019-03-01

© 2019 Walter de Gruyter GmbH, Berlin/Boston

Downloaded on 16.9.2025 from https://www.degruyterbrill.com/document/doi/10.1515/anly-2018-0046/html
Scroll to top button