The Gaussian function is a mathematical function that describes a symmetrical, bell-shaped curve. It is defined by the formula f(x) = a e^-\frac{(x-b)^22c^2} , where a determines the height, b is the center, and c controls the width of the curve. This function is widely used in statistics, physics, and engineering to model normal distributions and various natural phenomena. In statistics, the normal distribution is a key application of the Gaussian function, representing how data points are distributed around a mean. The properties of the Gaussian function make it essential in fields like signal processing and machine learning, where it helps in tasks such as data smoothing and pattern recognition.