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Gamma, Beta, Erf > FresnelS[z] > Introduction to the Fresnel integrals

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 :