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mathematical physics > differential operator > homogeneous function

mathematical analysis > functional analysis > operator > differential operator > homogeneous function

mathematical analysis > real analysis > real-valued function > function of several real variables > homogeneous function

Preferred term

homogeneous function

Definition(s)

In mathematics, a homogeneous function is a function of several variables such that, if all its arguments are multiplied by a scalar, then its value is multiplied by some power of this scalar, called the degree of homogeneity, or simply the degree; that is, if $k$ is an integer, a function $f$ of $n$ variables is homogeneous of degree $k$ if

${\\displaystyle f(sx_{1},\\ldots ,sx_{n})=s^{k}f(x_{1},\\ldots ,x_{n})}$

for every ${\\displaystyle x_{1},\\ldots ,x_{n},}$ and ${\\displaystyle s\ eq 0.}$
For example, a homogeneous polynomial of degree $k$ defines a homogeneous function of degree $k$ .
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Homogeneous_function)

Broader concept(s)

In other languages

fonction homogène

French

URI

http://data.loterre.fr/ark:/67375/PSR-NLK2W2WF-H

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