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

Representations through more general functions

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 :

Representations through related equivalent functions

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

Representations through other probability integrals and inverses

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