Gaussian Function
A Gaussian function, named after Carl Friedrich Gauss, is a specific type of mathematical function shaped like a symmetric bell curve. It is widely used in statistics, physics, signal processing, and image processing, with the normal distribution being its most famous application. The function is defined by parameters for its center, peak height, and width.
Background
The Gaussian function is the bell-shaped curve (e^(-x²)) that appears everywhere in science and engineering. It describes normal distributions in statistics, point-spread functions in optics, blur kernels in image processing, radial basis functions in machine learning, and wave packets in quantum mechanics. The Fourier transform of a Gaussian is also a Gaussian — a unique property that makes it central to signal processing and the Heisenberg uncertainty principle. The function is named after Carl Friedrich Gauss, though it was known to de Moivre earlier. Its integral is the square root of π, which ties it to the error function (erf) used in probability and statistics.