homogeneous function

homogeneous function

English

Noun

homogeneous function (plural homogeneous functions)

1. (mathematics) homogeneous polynomial
2. (mathematics) the ratio of two homogeneous polynomials, such that the sum of the exponents in a term of the numerator is equal to the sum of the exponents in a term of the denominator.

   ${\\displaystyle {\\frac {x^{3}+xy^{2}+x^{2}y+y^{3}}{z^{3}}}}$

3. (mathematics) a function f(x) which has the property that for any c, ${\\displaystyle f(cx)=cf(x)}$.