An asymptotic estimate of the integral of the product of two modified Bessel functions and a power function
type: Item
instance of: scholarly article
title: An asymptotic estimate of the integral of the product of two modified Bessel functions and a power function
zbMATH Open document ID: 0919.33001
DOI: 10.1007/BF02355423
author: R. N. Miroshin
published in: Mathematical Notes
publication date: 1999-01-11T00:00:00Z
review text: This paper is concerned with the estimate as \(\rho\uparrow 1\) of the integral \[ I_a^\rho(\mu,\nu)= \int_0^\infty x^{-\rho} K_{i\mu}(x) K_{i\nu}(ax) dx, \] where \(K_{i\mu}(x)\) is the modified Bessel function, \(a>0\), \(\mu>0\) and \(\nu>0\). The author gives the leading term of the asymptotics of this integral, which is useful in probability theory and has been known for a long time only in the particular case \(a=1\).
Mathematics Subject Classification ID: 33C10
Mathematics Subject Classification ID: 41A60
Mathematics Subject Classification ID: 60J99
zbMATH DE Number: 1238075
zbMATH Keywords: asymptotic estimate
zbMATH Keywords: Markov process
zbMATH Keywords: Bessel function
reviewed by: Luigi Gatteschi
MaRDI profile type: Publication
cites work: Q3957713
cites work: Q5519244
cites work: Q3265950
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description: scientific article; zbMATH DE number 1238075