Transcendental functions are those functions that do not satisfy an algebraic equation.

A function $f(x)$ is transcendental if there it does not satisfy an algebraic equation. These extend the notion of transcendental (and algebraic) numbers. Examples include $e^x,\sin(x),\log(x)$; non-examples include polynomials, radicals, rational functions, and characteristic functions; note that non-transcendental (i.e., algebraic) functions need not be elementary.

This tag should often be used for questions asking whether a function is transcendental. In particular, the indefinite integral of an algebraic function, such as $\int 1/x \,dx$, is often transcendental.