Special function
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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.