A note on the singular points of the function generated by the Bergman operator of the second kind

Abstract

Let ψ = P 2 ( f ) \psi = {P_2}(f) be Bergman’s operator of the second kind, f ( q ) f(q) is analytic at q = 0 q = 0 . In a previous paper [5] a theorem was obtained on the singularities of ψ \psi when ψ \psi was generated by a f ( q ) f(q) whose only singular points were poles. In this note we obtain a theorem on the singularities of ψ \psi when ψ \psi is generated by a f ( q ) f(q) whose singular points can be of more varied types.