Error Bounds for Asymptotic Expansions of Hankel Transforms

Abstract

An explicit expression is derived for the error term associated with the asymptotic expansions of the Hankel transform \[ I(x)\int_0^\infty {J_\nu (xt)q(t)dt} ,\] where $J_\nu (t)$ is the Bessel function of the first kind and x is a large positive parameter. From the explicit expression, realistic error bounds are also obtained.