Two infinite integrals of products of modified Bessel functions and powers of logarithms
type: Item
instance of: scholarly article
title: Two infinite integrals of products of modified Bessel functions and powers of logarithms
zbMATH Open document ID: 0836.33001
DOI: 10.1016/0377-0427(94)00075-0
author: K. S. Kölbig
published in: Journal of Computational and Applied Mathematics
publication date: 1996-02-01T00:00:00Z
review text: Starting from known integrals of Bessel functions new forms are derived that contain powers of logarithms. A typical example is \(\int_0^\infty t^{\rho-1} K_\nu (at) K_\lambda (at) \ln^m t dt\). When \(\nu\), \(\lambda\) are integers or half-integers the integrals can often be expressed in terms of finite sums. Several tables are given for these special cases.
Mathematics Subject Classification ID: 33C10
Mathematics Subject Classification ID: 33B15
zbMATH DE Number: 825301
zbMATH Keywords: gamma function
zbMATH Keywords: infinite integrals
zbMATH Keywords: integrals of Bessel functions
zbMATH Keywords: powers of logarithms
zbMATH Keywords: tables
reviewed by: Nico M. Temme
MaRDI profile type: Publication
full work available at URL: 0377-0427(94)00075-0
OpenAlex ID: W2041230192
cites work: Q3331506
cites work: Q3219281
cites work: Q3671491
cites work: On the Integral � ∞ 0 e -μt t t ν- 1 log m t dt
cites work: Q3999269
cites work: Q5562752
description: scientific article; zbMATH DE number 825301