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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.
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