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

  • Derek Naylor EMAIL logo
Veröffentlicht/Copyright: 15. Februar 2019
Analysis
Aus der Zeitschrift Analysis Band 39 Heft 1

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. Suche in Google Scholar

[2] G. Doetsch, Handbuch der Laplace-Transformation. Band 1, Birkhäuser, Basel, 1955. 10.1007/978-3-0348-4147-4Suche 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. 10.1007/978-3-662-11761-3Suche 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/22.2.129Suche in Google Scholar

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

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

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