Wolfram Researchfunctions.wolfram.comOther Wolfram Sites
Search Site
Function CategoriesGraphics GalleryNotationsGeneral IdentitiesAbout This Site Email Comments

View Related Information In
The Documentation Center

Download All Formulas For This Function
Mathematica Notebook
PDF File


Developed with Mathematica -- Download a Free Trial Version

General Identities

General Mathematical Identities for Analytic Functions

General Identities

Integral representations

Fourier integral representations

The Fourier integral is the continuous analogue of a Fourier series. This formulas can be derived from the Fourier series expansion of the function on interval as .

The substitution of and into the integral gives the following Fourier integral formulas:

The first definition can be rewritten in exponential form, leading to exponential direct and inverse Fourier transforms:

If the function is absolutely integrable on the real axis, you have the following equality: