A note on separation of variables
Yonah Cherniavsky · International Journal of Mathematical Education in Science and Technology · 2010
We write down very simple, necessary and sufficient conditions for the additive and multiplicative separability of variables: v(x 1, x 2, … , x n ) = g 1(x 1) + g 2(x 2) + · · · + g n (x n ) or u(x 1, x 2, … , x n ) = f 1(x 1)f 2(x 2) · · · f n (x n ).