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Erfc






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





Connections within the group of probability integrals and inverses and with other function groups


The probability integrals , , , and are the particular cases of two more general functions: hypergeometric and Meijer G functions.

For example, they can be represented through the confluent hypergeometric functions and :

Representations of the probability integrals , , , and through classical Meijer G functions are rather simple:

The factor in the last four formulas can be removed by changing the classical Meijer G functions to the generalized one:

The probability integrals , , , and are the particular cases of the incomplete gamma function, regularized incomplete gamma function, and exponential integral :

The probability integrals , , and can be represented through Fresnel integrals by the following formulas:

The probability integrals and their inverses , , , , , , and are interconnected by the following formulas:





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