adj. 1. (of a series) such that the series of absolute values of its terms converges; then Σ a_i is said to converge absolutely to s, where s is the sum of the terms, a_i, of the given series, rather than of their absolute values, |a_i|. For example, is absolutely convergent, since but is not absolutely convergent, since diverges. See also comparison test. 2. (of an infinite product) such that the logarithms of the successive terms form an absolutely convergent series. Compare conditionally convergent.