Difference between revisions of "Algebraic functions"
BRichtigen (talk | contribs) (New page: 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(...) |
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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>. | + | 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. | 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. | ||
Revision as of 21:29, November 27, 2008
An algebraic function is a function Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle y = f(x)} which satisfies a polynomial equation Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle p(x,y) = 0} .
Alternatively, Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle a_n(x) y^n + a_{n-1}(x) y^{n-1} + a_1(x) y + a_0(x) = 0} , where Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 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.