# nLab elementary function

Elementary functions are the functions of one complex variable obtained from the identy function? $x$, the (possibly fractional) power function?s ${x}^{\gamma }$, trigonometric function?s, the exponential functions and logarithmic function?s by the algebraic operations (addition, subtraction, multiplication, division) and composition. Elementary functions form a well-defined class. Some of them are multivalued and have singular points (e.g. the square root ${x}^{1/2}$ has a branch point? at the origin).

Functions of a complex variable which are not elementary are sometimes called transcendental, although usually this term is used for the (strictly larger) class of functions that are not algebraic?.

Revised on October 23, 2011 01:09:01 by Toby Bartels (67.141.101.96)