Difference between revisions of "Algebraic functions"

Latest revision as of 23:07, March 1, 2021

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

Alternatively, $a_{n}(x)y^{n}+a_{n-1}(x)y^{n-1}+a_{1}(x)y+a_{0}(x)=0$ , 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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-An '''algebraic function''' is a function <math>y = f(x)</math> which satisfies  a [[polynomial]] equation <math>p(x,y) = 0</math>. Yeah, you didn't understand that either, did you.
+An '''algebraic function''' is a function <math>y = f(x)</math> which satisfies  a [[polynomial]] equation <math>p(x,y) = 0</math>.
+Alternatively, <math>a_n(x) y^n + a_{n-1}(x) y^{n-1} + a_1(x) y + a_0(x) = 0</math>, where <math> a_n(x), a_{n-1}(x), \cdots, a_1(x),   a_0(x)</math> are themselves polynomials in x.
 A function which is not algebraic is called a [[Transcendental functions|transcendental function]].
-[[Category:Mathematics]]
+[[Category:Algebra]]