Definition:Fresnel Integral

Definition

Fresnel Sine Integral Function

The Fresnel sine integral function is the real function $\operatorname S: \R \to \R$ defined by:

$\ds \map {\operatorname S} x = \sqrt {\frac 2 \pi} \int_0^x \sin u^2 \rd u$

Fresnel Cosine Integral Function

The Fresnel cosine integral function is the real function $\operatorname C: \R \to \R$ defined by:

$\ds \map {\operatorname C} x = \sqrt {\frac 2 \pi} \int_0^x \cos u^2 \rd u$

Also see

• Results about Fresnel integrals can be found here.

Source of Name

This entry was named for Augustin-Jean Fresnel.

Historical Note

The Fresnel integrals were used by Augustin-Jean Fresnel to analyse the diffraction of light.

Linguistic Note

The eponym Fresnel is pronounced fre-nell.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Fresnel integrals
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Fresnel integrals

• Weisstein, Eric W. "Fresnel Integrals." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/FresnelIntegrals.html