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High Quality Content by WIKIPEDIA articles! A transcendental function is a function that does not satisfy a polynomial equation whose coefficients are themselves polynomials, in contrast to an algebraic function, which does satisfy such an equation. In other words a transcendental function is a function which "transcends" algebra in the sense that it cannot be expressed in terms of a finite sequence of the algebraic operations of addition, multiplication, and root extraction. Examples of transcendental functions include the exponential function, the logarithm, and the trigonometric functions. Formally, an analytic function ?(z) of one real or complex variable z is transcendental if it is algebraically independent of that variable.