absolutely convergent

adjective

, Mathematics.

1. of or characterized by absolute convergence.

absolutely convergent

/ ăb′sə-lo̅o̅t′lē /

1. Relating to or characterized by absolute convergence.

Example Sentences

Within a common circle of convergence two power series Σ anzn, Σ bnzn can be multiplied together according to the ordinary rule, this being a consequence of a theorem for absolutely convergent series.

From Project Gutenberg

The great merit of asymptotic expansions is that they admit of addition, subtraction, multiplication and division, term by term, in the same way as absolutely convergent series, and they admit also of integration term by term; that is to say, the results of such operations are asymptotic expansions for the sum, difference, product, quotient, or integral, as the case may be.

From Project Gutenberg

The series is also convergent if the real series formed by the moduli of its terms is convergent; in that case the series is said to be absolutely convergent, and it can be shown that its sum is unaltered by taking the terms in any other order.

From Project Gutenberg