A note on a modified Bessel function integral

2015/10/01 by Paris, R. B.
#30E20 #33C10 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1510.00192

Abstract

We investigate the integral ∫₀^∞ \cosh^μ t K_ν(z\cosh t) dt \Re(z)gt;0, where K denotes the modified Bessel function, for non-negative integer values of the parameters μ and ν. When the integers are of different parity, closed-form expressions are obtained in terms of z^-1e^-z multiplied by a polynomial in z^-1 of degree dependent on the sign of μ-ν.

Related

• On the ν-zeros of the modified Bessel function K_iν(x) of positive argument
• Asymptotics of some integrals involving modified Bessel and hyper-Bessel functions
• Modified Bessel Functions in Analytic Number Theory
• Inequalities for an integral involving the modified Bessel function of the first kind
• The asymptotic expansion of Kratzel's integral and an integral related to an extension of the Whittaker function