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Zbl 0692.44004
Naylor, Derek
On an asymptotic expansion of the Kontorovich-Lebedev transform. (English)
[J] Appl. Anal. 39, No.4, 249-263 (1990). ISSN 0003-6811; ISSN 1563-504X/e

An asymptotic expansion valid for large positive values of the parameter s is constructed for the integral transform $F(s)=\int\sp{\infty}\sb{0}K\sb{is}(x)f(x)dx/x$ where $K\sb{is}(x)$ denotes the modified Bessel function of the third kind of purely imaginary order. \par Editorial remark: According to {\it S. Yakubovich} [C. R., Math., Acad. Sci. Paris 350, No. 3-4, 147 (2012; Zbl 06017088)], there is a gap on on p. 260 concerning the formula (1.9).
[D.Naylor]

MSC 2000:: *44A15 Special transforms
41A60 Asymptotic problems in approximation

Keywords: Kontorovich-Lebedev transform; asymptotic expansion; Bessel function

Citations: Zbl 06017088

Cited in: Zbl 1218.42001 Zbl 1059.44002 Zbl 1007.44002 Zbl 0980.41027

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