Connection factors in the Schrödinger equation with a polynomial potential

Given a second order differential equation with two singular points, namely the origin and infinity, the connection factors allow to split a power series solution into formal solutions with known asymptotic behavior. A procedure is suggested to obtain those factors, as quotients of Wronskians of the mentioned solutions, in the case of a Schrödinger equation with a polynomial potential. Application of the procedure to particular cases, whose connection factors are already known, allows us to obtain new relations for quotients and products of gamma functions.