Algebraic Function
An algebraic function is a function f(x) which satisfies p(x,f(x))=0, where p(x,y) is a polynomial in x and y 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.
See also
Algebraic Equation, Elementary Function, Elementary Operation, Transcendental FunctionExplore with Wolfram|Alpha
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References
Flajolet, P. and Sedgewick, R. "Analytic Combinatorics: Functional Equations, Rational and Algebraic Functions." https://inria.hal.science/inria-00072528v1.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 Resource. https://mathworld.wolfram.com/AlgebraicFunction.html