Green's function for a Schroedinger operator and some related summation formulas
arXiv:math-ph/0505070 · doi:10.1063/1.1952581
Abstract
Summation formulas are obtained for products of associated Lagurre polynomials by means of the Green's function K for the Hamiltonian H = -{d^2\over dx^2} + x^2 + Ax^{-2}, A > 0. K is constructed by an application of a Mercer type theorem that arises in connection with integral equations. The new approach introduced in this paper may be useful for the construction of wider classes of generating function.
14 pages