Neat Summation Notation for Multivariate Polynomials

Question

For a single-variable polynomial we can write it nicely in summation notation as $$p(x)=\sum_{k=0}^n a_kx^k$$.

How about multivariate polynomials, for instance $p(x,y,z)$? Is there any neat notation to describe a typical polynomial?

Thanks.

Answer 1

Yeah, you can write it as

$$p(x,y,z) = \sum_{i=0}^{n_1}\sum_{j=0}^{n_2}\sum_{k=0}^{n_3} a_{i,j,k}x^iy^jz^k$$