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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 Function

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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.

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Algebraic Function

Cite this as:

Weisstein, Eric W. "Algebraic Function." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/AlgebraicFunction.html

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