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Gamma, Beta, Erf > InverseErf[z] > Introduction to the probability integrals and inverses

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.