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:
