Special functions are mathematical functions that arise in various areas of science and engineering. They often have unique properties and are used to solve specific types of problems, particularly in calculus, physics, and statistics. Examples include the Bessel functions, Legendre polynomials, and Gamma function, each serving important roles in different applications. These functions are typically defined by specific equations or series and can be more complex than standard functions like polynomials or exponentials. They help in modeling phenomena such as wave propagation, heat conduction, and quantum mechanics, making them essential tools in both theoretical and applied mathematics.