The error function (often denoted *erf(x)*) and the complementary error function (often denoted *erfc(x)*) occur frequently in solutions to integral equations and is familiar to statisticians as well. The error function may be defined as

/ x
erf(x) = 2/sqrt(pi) * | exp(-y^2) dy
/ 0
erf(-x) = -erf(x)
erfc(x) = 1-erf(x)