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)

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