An Etymological Dictionary of Astronomy and Astrophysics

Two integrals that involve quadratic equations in the sine and cosine functions and are defined as:

C(x) = ∫ cos (πt²/2) dt and

C(y) = ∫ sin (πt²/2) dt, integrated from 0 to x.

They are quite frequently used in optics studying → Fresnel diffraction and similar topics. The Fresnel integrals are also used in railway and freeway constructions.
These integrals may be evaluated to arbitrary precision using → power series. Alternatively the amplitudes may be found graphically by use of → Cornu’s spiral.

See also: → Fresnel diffraction; → integral.