absolutely convergent series

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• Convergent series — redirects here. For the short story collection, see Convergent Series (short story collection). In mathematics, a series is the sum of the terms of a sequence of numbers. Given a sequence , the nth partial sum Sn is the sum of the first n terms… …   Wikipedia

• absolutely convergent — adjective of an infinite series : remaining convergent even if the signs of negative terms are changed …   Useful english dictionary

• 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

• absolutely — adverb Date: 14th century 1. in an absolute manner or condition often used as an intensive < absolutely brilliant > 2. with respect to absolute values < an absolutely convergent series > …   New Collegiate Dictionary

• Alternating series — In mathematics, an alternating series is an infinite series of the form:sum {n=0}^infty ( 1)^n,a n,with an ≥ 0 (or an ≤ 0) for all n . A finite sum of this kind is an alternating sum. An alternating series converges if the terms an converge to 0… …   Wikipedia

• Dirichlet series — In mathematics, a Dirichlet series is any series of the form where s and an are complex numbers and n = 1, 2, 3, ... . It is a special case of general Dirichlet series. Dirichlet series play a variety of important roles in analytic number theory …   Wikipedia

• Power series — In mathematics, a power series (in one variable) is an infinite series of the form:f(x) = sum {n=0}^infty a n left( x c ight)^n = a 0 + a 1 (x c)^1 + a 2 (x c)^2 + a 3 (x c)^3 + cdotswhere an represents the coefficient of the n th term, c is a… …   Wikipedia

• Grandi's series — The infinite series 1 − 1 + 1 − 1 + hellip;or:sum {n=0}^{infin} ( 1)^nis sometimes called Grandi s series, after Italian mathematician, philosopher, and priest Guido Grandi, who gave a memorable treatment of the series in 1703. It is a divergent… …   Wikipedia

• exponential series — noun a series derived from the expansion of an exponential expression • Hypernyms: ↑series * * * noun : a series derived from the development of exponential expressions; specifically : the fundamental expansion ex = 1 + x/1 + x²/2! + x³/3!+…,… …   Useful english dictionary

• Fourier series — Fourier transforms Continuous Fourier transform Fourier series Discrete Fourier transform Discrete time Fourier transform Related transforms …   Wikipedia

• Absolute convergence — In mathematics, a series (or sometimes also an integral) of numbers is said to converge absolutely if the sum (or integral) of the absolute value of the summand or integrand is finite. More precisely, a real or complex series is said to converge… …   Wikipedia