Definition:Algebraic Function/Real
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Definition
Let $y$ be a solution to the polynomial equation:
- $\map {p_0} x + \map {p_1} x y + \dotsb + \map {p_{n - 1} } x y^{n - 1} + \map {p_n} x y^n = 0$
where $\map {p_0} x \ne 0, \map {p_1} x, \dotsc, \map {p_n} x$ are real polynomial functions in $x$.
Then $y = \map f x$ is a (real) algebraic function:
Also see
- Results about algebraic functions can be found here.
Sources
- 1973: G. Stephenson: Mathematical Methods for Science Students (2nd ed.) ... (previous) ... (next): Chapter $1$: Real Numbers and Functions of a Real Variable: $1.3$ Functions of a Real Variable: $\text {(f)}$ Algebraic Functions $(8)$