Explicit forms of the off-shell Jost solutions for general central potentials

We derive explicit forms of the regular solutions and the Jost solutions off the energy shell, which satisfy the inhomogeneous Schrödinger equation. The used forms of the Yukawa-like and Gauss-like potentials are related to the two known integral representations of the Hankel functions. The explicit form of the introduced fully off-shell Jost functions enables us to write it in the alternative integral forms, which contain the Jost solutions or the regular solution.