Evaluation of Generalized Error Function via Fast-Converging Power Series

A generalized form of the error function, $G_p\left(x\right)=\frac{p}{\Gamma \left(1/p\right)}{\displaystyle {\int }_0^x{\text{e}}^{？t^p}\text{d}t}$ , which is directly associated with the gamma function, is evaluated for arbitrary real values of $p>1$ and $0<x\le +\infty$ 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.