I am familiar with polynomials, for example, f_{1}(x) = a_{0 }x^{0}+ a_{1 }x^{1}+ a_{2 }x^{2}+ a_{3 }x^{3}+ ...

where the a_{i}are constant coefficients.

But now I am wondering what the correct terminology is for an equation with mixed terms.

For example, say you have a function of two variables f(x, y), three variables f(x, y, z), or more. Something like the following:

f_{2}(x,y) = a_{0 }x^{0}+ a_{1 }xy + a_{2 }x^{2}y + a_{3}x^{3}y + a_{4 }xy^{4}+ a_{5 }x^{2}y^{2 }Basically, the equation is comprised of a bunch of mixed terms, but no transcendentals.

Does this sort of equation have a name when it is being discussed?