A note on a modified Bessel function integral

Abstract

We investigate the integral \[\int_0^\infty \cosh^μ\!t\,K_ν(z\cosh t)\,dt \qquad \Re(z)>0,\] where $K$ denotes the modified Bessel function, for non-negative integer values of the parameters $\mu$ and $\nu$. When the integers are of different parity, closed-form expressions are obtained in terms of $z^{-1}{e}^{-z}$ multiplied by a polynomial in $z^{-1}$ of degree dependent on the sign of $\mu -\nu$.

6 pages

References in corpus (3)

• Relic Neutrino Freeze-out: Dependence on Natural Constants
• Non-Equilibrium Aspects of Relic Neutrinos: From Freeze-out to the Present Day
• A Recursive Method for Computing Certain Bessel Function Integrals