Green's function for a Schrödinger operator and some related summation formulas

Summation formulas are obtained for products of associated Lagurre polynomials by means of the Green's function K for the Hamiltonian H0=−d2∕dx2+x2+Ax−2 (A>0). K is constructed by an application of a Mercer-type theorem that arises in connection with integral equations. The approach introduced in this paper may be useful for the construction of wider classes of generating function.