Gaussian function is named after the great mathematician Johann Carl Friedrich Gauss. Gaussian function is widely used in natural science, social science, mathematics and engineering.

The graph of Gaussian function is like an inverted clock in shape. Parameter A refers to the peak of gaussian curve, B is its corresponding abscissa, and C is the standard deviation (sometimes called Gaussian root mean square width), which controls the width of the "clock".

Application:

The indefinite integral of Gaussian function is an error function. Gaussian function exists in natural science, social science, mathematics and engineering. Examples in this respect include:

In statistics and probability theory, Gaussian function is a density function of normal distribution, and it is a finite probability distribution of complex sum according to the central limit theorem.

Gaussian function is the wave function of the ground state of quantum harmonic oscillator.

Molecular orbitals used in computational chemistry are linear combinations of Gaussian functions, called Gaussian orbitals (see basis sets in quantum chemistry).

In the field of mathematics, Gaussian function plays an important role in the definition of Hermite polynomial.

Gaussian function in quantum field theory is related to vacuum state.

Gaussian beams have applications in optical and microwave systems.

Gaussian function is used as a pre-smoothing kernel in image processing (see scale space representation).