The Singular Points of Analytic Functions with Finite X-Order Defined by Laplace-Stieltjes Transformations

We study the singular points of analytic functions defined by Laplace-Stieltjes transformations which converge on the right half plane, by introducing the concept of X-order functions. We also confirm the existence of the finite X-order Borel points of such functions and obtained the extension of the finite X-order Borel point of two analytic functions defined by two Laplace-Stieltjes transformations convergent on the right half plane. The main results of this paper are improvement of some theorems given by Shang and Gao.