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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

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 ).

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