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

Abstract:

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