Evaluation of Generalized Error Function via Fast-Converging Power Series

Abstract

A generalized form of the error function, G p ( x ) = p Γ ( 1 / p ) ∫ 0 x e − t p d t , which is directly associated with the gamma function, is evaluated for arbitrary real values of p > 1 and 0 < x ≤ + ∞ by employing a fast-converging power series expansion developed in resolving the so-called Grandi’s paradox. Comparisons with accurate tabulated values for well-known cases such as the error function are presented using the expansions truncated at various orders.