Inequalities for an integral involving the modified Bessel function of the first kind

Robert E. Gaunt

Simple bounds are obtained for the integral ${\int }_0^x{\mathrm{e}}^{-\gamma t}{t}^{\nu }{I}_{\nu }(t)\mathrm{d}t$, $x>0$, $\nu >-1/2$, $0\le \gamma <1$, together with a natural generalisation of this integral.…