absolute convergence of infinite product and series
Theorem. The infinite product
converges absolutely (http://planetmath.org/AbsoluteConvergenceOfInfiniteProduct) if and only if the series
with complex converges absolutely (http://planetmath.org/AbsoluteConvergence).
Proof. The theorem follows directly from the theorems of the entries absolutely convergent infinite product converges and infinite product of sums (http://planetmath.org/InfiniteProductOfSums1a_i).