Definitions of probability integrals and inverses

The probability integral (error function) , the generalized error function , the complementary error function , the imaginary error function , the inverse error function , the inverse of the generalized error function , and the inverse complementary error function are defined through the following formulas:

These seven functions are typically called probability integrals and their inverses.

Instead of using definite integrals, the three univariate error functions can be defined through the following infinite series.