Summability Test for Multidimensional Singular Points

Abstract

The closest singular point to the origin of the following power series f(z) = P∞ n=0 anz n is on the convergence disc. However, there is a difficulty when one tries to identify or pinpoint which point, particularly on the disc of convergence, is found to be a singular point. In 1965 J.P. King established tests using Taylor and Euler summability methods to identify singular points of power series. The goal, motivation, and objective behind this paper include, but are not limited to, the presentation of double sequence notions and the establishment of multidimensional analogs of summability tests presented in J.P. King’s singular points for a double power series. The methodology in achieving this goal applied Hamilton’s [2] methods to two dimensional tests for singularity.