Special function

Special functions is class of mathematical functions with established definitions and known properties.

The important class of special functions is elementary functions.

Usually, a special function is defined as a solution of a simple differential equation or an integral of an elementary function, or an inverse function of some elementary function.

Usually, a special function is holomorphic on some domain of the complex plane.

Also, many special functions are real, id est, have real values at the real values of the argument.