Borel-summable series

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• Series (mathematics) — A series is the sum of the terms of a sequence. Finite sequences and series have defined first and last terms, whereas infinite sequences and series continue indefinitely.[1] In mathematics, given an infinite sequence of numbers { an } …   Wikipedia

• History of Grandi's series — Geometry and infinite zerosGrandiGuido Grandi (1671 – 1742) reportedly provided a simplistic account of the series in 1703. He noticed that inserting parentheses into nowrap|1=1 − 1 + 1 − 1 + · · · produced varying results: either:(1 1) + (1 1) + …   Wikipedia

• Divergent geometric series — In mathematics, an infinite geometric series of the form is divergent if and only if | r | ≥ 1. Methods for summation of divergent series are sometimes useful, and usually evaluate divergent geometric series to a sum that… …   Wikipedia

• Summation of Grandi's series — General considerationstability and linearityThe formal manipulations that lead to 1 − 1 + 1 − 1 + · · · being assigned a value of 1⁄2 include: *Adding or subtracting two series term by term, *Multiplying through by a scalar term by term, *… …   Wikipedia

• 1 − 2 + 3 − 4 + · · · — In mathematics, 1 − 2 + 3 − 4 + … is the infinite series whose terms are the successive positive integers, given alternating signs. Using sigma summation notation the sum of the first m terms of the series can be expressed as:sum {n=1}^m n( 1)^{n …   Wikipedia

• 1 − 2 + 4 − 8 + · · · — In mathematics, 1 − 2 + 4 − 8 + hellip; is the infinite series whose terms are the successive powers of two with alternating signs. As a geometric series, it is characterized by its first term, 1, and its common ratio, −2. :sum {i=0}^{n} ( 2)^iAs …   Wikipedia

• Cesàro summation — For the song Cesaro Summability by the band Tool, see Ænima. In mathematical analysis, Cesàro summation is an alternative means of assigning a sum to an infinite series. If the series converges in the usual sense to a sum A, then the series is… …   Wikipedia

• Lp space — In mathematics, the Lp spaces are function spaces defined using a natural generalization of the p norm for finite dimensional vector spaces. They are sometimes called Lebesgue spaces, named after Henri Lebesgue (Dunford Schwartz 1958, III.3),… …   Wikipedia

• 1 − 2 + 3 − 4 + · · · — Série alternée des entiers Les premiers milliers de termes et de sommes partielles de 1 − 2 + 3 − 4 + … La série alternée des entiers est, en mathématiques, la série associée à la suite des nombres entiers (strictement positifs), affectés de… …   Wikipédia en Français

• Série alternée des entiers — Traduction à relire 1 − 2 + 3 − 4 …   Wikipédia en Français

• 1 − 2 + 3 − 4 + · · · — Los primeros miles de términos y sumas parciales de 1 − 2 + 3 − 4 + · · ·. En matemáticas, la expresión 1 − 2 + 3 − 4 + · · · es una serie infin …   Wikipedia Español