Connections within the group of Fresnel integrals and with other function groups

Representations through more general functions

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

For example, they can be represented through regularized hypergeometric functions :

These two integrals can also be expressed through generalized and classical Meijer G functions:

The first two formulas are simpler than the last two classical representations (which include factors like ).

Representations through related equivalent functions

The Fresnel integrals and can be represented through a combination of probability integrals with corresponding values of , , and :