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单词 AbsoluteConvergenceOfInfiniteProductAndSeries
释义

absolute convergence of infinite product and series


Theorem.  The infinite product

n=1(1+cn)

converges absolutely (http://planetmath.org/AbsoluteConvergenceOfInfiniteProduct) if and only if the series

n=1cn

with complex cn 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 1+ai (http://planetmath.org/InfiniteProductOfSums1a_i).

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