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We evaluate the short-range asymptotic behavior of Green's function for aHamiltonian when its potential energy part has an inverse power singularity atthe origin. The analytically solvable case of sharply screened Coulombpotential is considered firstly. For this potential the additional logarithmicsingular term has been found in the short-range asymptote of the Green functionas in the case of the pure Coulomb potential. The case of a short-rangepotential of an arbitrary form with inverse power singularity is treated on thebasis of the integral Lippmann-Schwinger equation. It is shown that, if thesingularity is weaker than the Coulomb one, the Green function has onlystandard singularity. For the case of $r^{-\rho}$ singularity of the potentialwith $1\le\rho<2$ the additional singularity in the asymptotic behavior of theGreen function appears. In the case of $\rho=1$ the additional logarithmicsingularity has the same form as in the case of the pure Coulomb potential. Inthe case of $1<\rho<2$ the additional singularity of the Green function has theform of the polar singularity $r^{-\rho+1}$. These results are applied forextending the zero-range potential formalism on Hamiltonians with singularpotentials.

On Green's functions for Hamiltonians with potentials possessing singularity at the origin: application to the zero-range potential formalism