For example, the roots of any quadratic equation with complex
coefficients can be expressed in closed form in terms of
addition, subtraction, multiplication, division, and square root
extraction, all elementary functions. However, there are quintic
equations without closed-form solutions using elementary
functions — see Galois theory. Changing the definition of "well-
known" to include additional functions can change the set of
equations with closed-form solutions. Many cumulative
distribution functions cannot be expressed in closed form,
unless one considers special functions such as the error
function or gamma function to be well-known. It is possible to
solve the quintic equation if general hypergeometric functions
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 well-known, since
numerical implementations are widely available.