Noun
(mathematical analysis) Any function that is algebraically independent of its variable(s); a function which does not satisfy a polynomial equation whose coefficients are themselves polynomials.
An analytic function is transcendental (i.e., is a transcendental function) if and only if its Riemann surface is noncompact.
(specifically, complex analysis) A meromorphic function on the complex plane that is not a rational function.
Source: en.wiktionary.org