double sum

A double sum is a series having terms depending on two indices, sum_(i, j) b_(i j). A finite double series can be written as a product of series sum_(i = 1)^m sum_(j = 1)^n x_i y_j | = | x_1 y_1 + x_1 y_2 + ... + x_2 y_1 + x_2 y_2 + ... | = | (x_1 + x_2 + ... + x_m) y_1 + (x_1 + x_2 + ... + x_m) y_2 + ... | = | ( sum_(i = 1)^m x_i)(y_1 + y_2 + ... + y_n) | = | ( sum_(i = 1)^m x_i)( sum_(j = 1)^n y_j).

Euler sum | Madelung constants | multiple series | multivariate zeta function | series | triple series | Weierstrass's double series theorem