A Method for the Computation of the Error Function of a Complex Variable

This paper presents a method of computing $z \equiv \left ( {2/\sqrt \pi } \right )\int _0^z {{e^{ - {u^2}}}du}$, where $z$ is complex. It is shown that $z \equiv 1 - {\text {erf }}z$ has no zeros in the right-hand half plane. An estimate of $|{\text {erfc }}z|$ is derived.