Editing Closed-form expression (section)

== Alternative definitions ==

Changing the basic functions to include additional functions can change the set of equations with closed-form solutions.  Many [[cumulative distribution function]]s cannot be expressed in closed form, unless one considers [[special functions]] such as the [[error function]] or [[gamma function]] to be basic.  It is possible to solve the quintic equation if general [[hypergeometric function]]s are included, although the solution is far too complicated algebraically to be useful.  For many practical computer applications, it is entirely reasonable to assume that the gamma function and other special functions are basic since numerical implementations are widely available.