# Category: Summability theory

Absolute convergence
In mathematics, an infinite series of numbers is said to converge absolutely (or to be absolutely convergent) if the sum of the absolute values of the summands is finite. More precisely, a real or com
Riemann series theorem
In mathematics, the Riemann series theorem (also called the Riemann rearrangement theorem), named after 19th-century German mathematician Bernhard Riemann, says that if an infinite series of real numb
Divergent series
In mathematics, a divergent series is an infinite series that is not convergent, meaning that the infinite sequence of the partial sums of the series does not have a finite limit. If a series converge
Abelian and Tauberian theorems
In mathematics, Abelian and Tauberian theorems are theorems giving conditions for two methods of summing divergent series to give the same result, named after Niels Henrik Abel and Alfred Tauber. The
Lévy–Steinitz theorem
In mathematics, the Lévy–Steinitz theorem identifies the set of values to which rearrangements of an infinite series of vectors in Rn can converge. It was proved by Paul Lévy in his first published pa
Unconditional convergence
In mathematics, specifically functional analysis, a series is unconditionally convergent if all reorderings of the series converge to the same value. In contrast, a series is conditionally convergent
Conditional convergence
In mathematics, a series or integral is said to be conditionally convergent if it converges, but it does not converge absolutely.
Mertens' theorems
In number theory, Mertens' theorems are three 1874 results related to the density of prime numbers proved by Franz Mertens. "Mertens' theorem" may also refer to his theorem in analysis.
Silverman–Toeplitz theorem
In mathematics, the Silverman–Toeplitz theorem, first proved by Otto Toeplitz, is a result in summability theory characterizing matrix summability methods that are regular. A regular matrix summabilit