A Gaussian function (the first syllable rhymes with house) is a function of the form
Gaussian functions with c2=2 are eigenfunctions of the Fourier transform.
Gaussian functions are among those functions that are "elementary" but lack "elementary antiderivatives", i.e., their antiderivatives are not among the functions ordinarily considered in first-year calculus courses. Nonetheless their definite integrals over the whole real line can be evaluated exactly.
The density function of the normal probability distribution is a Gaussian function.
See also: Lorentzian function