Integral representations of the Jost function

Abstract

Apparently different criteria are used to arrive at the integral representations of Jost functions. In dealing with this we present a guideline to rederive these results only from the Volterra integral equation satisfied by the Jost solutions. Both on- and off-shell Jost-type functions are considered. Using one of our formal results, we derive a useful expression for the s-wave Coulomb off-shell Jost solution.