Transcendental Function

A transcendental function is an analytic function that does not satisfy any polynomial equation whose coefficients can themselves be built from ordinary arithmetic, which sets it apart from algebraic functions, which do satisfy such an equation. The best known transcendental functions include the exponential functions, the trigonometric functions such as sine and cosine, the hyperbolic functions, and the logarithms, along with each of their inverses; more specialized examples include the gamma function, the error function, Bessel functions and the Riemann zeta function. What all of them share is that none can be built from addition, subtraction, multiplication, division and root extraction alone; each requires some limiting process, such as an infinite series or integral, to be properly defined, which is what makes transcendental functions a distinct and essential class alongside the algebraic functions. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/