Special functions
Categories: special functions
The articles in this section deal with special functions.
Special functions are functions that are reasonably well-known, but not quite as widely used as the very common functions such as trig functions or logarithms (which are known and elementary functions). There is no exact definition, to some extent it is a matter of opinion which set some functions belong to, but typically we say that:
- Elementary functions include the trig functions, inverse trig functions, exponentials, logarithms, the hyperbolic functions, and the inverse hyperbolic functions. They also include any other functions that are created by combining elementary functions.
- Special functions are other well-known functions such as the gamma function or the Lambert W function.
Special functions don't usually have a closed form, that is to say, they cannot usually be expressed in terms of elementary functions or constants. However, most of them have been widely studied over many years, so their characteristics are well known. In many cases, they are available on pocket calculators, and in the standard maths libraries of most programming languages.
This usually means that, if we obtain a solution in terms of a special function, then we can consider the problem solved.
See also
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