Algebraic functions

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An algebraic function is a function y = f(x) which satisfies a polynomial equation p(x,y) = 0.

Alternatively, an(x)yn + an − 1(x)yn − 1 + a1(x)y + a0(x) = 0, where  a_n(x), a_{n-1}(x), \cdots, a_1(x),   a_0(x) are themselves polynomials in x.

A function which is not algebraic is called a transcendental function.

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