Special function

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Special functions are a class of mathematical functions with established definitions and known properties; an important class are 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. There exist algorithms for the efficient evaluation. Some of special functions are implemented in the programming languages.

A special function is often 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.