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A special function is a function (usually named after an early investigator of its properties) having a particular use in mathematical physics or some other branch of mathematics.

** Special Function List**

Gamma function, Beta function, Pergeometric function, Whittaker function, Error function (also called the Gauss error function), Meijer G-function Bessel functions, Gauss hypergeometric function and the polynomials functions (Jacobi, Legendre, Laguerre, Hermite, etc.) are all the Special functions.

** Special Function is useful tools for solving differential equations**

Many special functions appear as solutions of differential equations or integrals of elementary functions.

Special functions are used as useful tools for solving ordinary and partial differential equations, as well as integral, differintegral, and integro-differential equations, fractional-calculus analogues and extensions of each of these equations, and various other problems involving special functions in mathematical physics and applied mathematics.

Special functions are particular mathematical functions that have more or less established names and notations due to their importance in mathematical analysis, functional analysis, geometry, physics, or other applications.

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