A method of computing the complex probability function and other related functions over the whole complex plane

Abstract

Using the symmetry relations of the complex probability function (CPF), the algorithm developed by Humlíček (1979) to compute this function over the upper half plane can be extended to cover the entire complex plane. Using the Humlíček algorithm the real and imaginary components of the CPF can be computed over the whole complex plane. Because of the relation between the CPF and other interesting mathematical functions, fast and accurate computer programs can be written to compute them. Such functions include the derivatives of the CPF, the complex error function, the complex Fresnel integrals, and the complex Dawson's functions. Fortran implementations of these functions are included in the Appendix.