Numerical Calculation of $\func{erf}x$

Aleksandar Donev - Dr. Phillip Duxbury

September 2000

In many physics applications involving the normal probability distribution function integrals of the form $\int_{-x}^{x}e^{-t^{2}/2}dt$ appear. This integral can not be solved in terms of standard transcendental and algebraic functions, so a new special function called the error function is introduced:

$$\func{erf}x=\frac{2}{\sqrt{\pi }}\int_{0}^{x}e^{-t^{2}}dt$$ (1)

The next few worksheets in this class will involve different ways of evaluating this function using Fortran 90. We will consider truncated power series as a means of evaluating . Notice that the argument of the error function can be a complex number, in which case the integral needs to be done in the complex plane.