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 :