An algebraic function is a function 
which satisfies 
, where 
is a polynomial in 
and 
with integer coefficients. Functions that can be constructed
using only a finite number of elementary operations
together with the inverses of functions capable
of being so constructed are examples of algebraic functions. Nonalgebraic functions
are called transcendental functions.
Algebraic Function
See also
Algebraic Equation, Elementary Function, Elementary Operation, Transcendental FunctionExplore with Wolfram|Alpha
References
Flajolet, P. and Sedgewick, R. "Analytic Combinatorics: Functional Equations, Rational and Algebraic Functions." http://www.inria.fr/RRRT/RR-4103.html.Knopp, K. "Algebraic Functions." Ch. 5 in Theory of Functions Parts I and II, Two Volumes Bound as One, Part II. New York: Dover, pp. 119-134, 1996.Koch, H. "Algebraic Functions of One Variable." Ch. 6 in Number Theory: Algebraic Numbers and Functions. Providence, RI: Amer. Math. Soc., pp. 141-170, 2000.Referenced on Wolfram|Alpha
Algebraic FunctionCite this as:
Weisstein, Eric W. "Algebraic Function." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/AlgebraicFunction.html