absolute convergence

American  

noun

Mathematics.

1. the property of an infinite series in which the series formed by replacing each term in the original series with its absolute value converges.

2. the property of a sequence of functions in which the series whose terms are the successive differences of the elements of the sequence exhibits absolute convergence.

3. the property of an improper integral in which the integral formed by replacing the integrand by its absolute value converges.

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absolute convergence Scientific  

/ ăb′sə-lo̅o̅t′ /

1. The mathematical property by which the sums of the absolute values of the terms in a series converge.

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Etymology

Origin of absolute convergence

First recorded in 1905–10

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How does absolute-convergence compare to similar and commonly confused words? Explore the most common comparisons:

• absolute convergence vs. conditional convergence