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infinite summation

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  • Summation — For evaluation of sums in closed form see evaluating sums. : Summation is also a term used to describe a process in synapse biology. Summation is the addition of a set of numbers; the result is their sum or total . The numbers to be summed may be …   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

  • Ewald summation — is a method for computing the interaction energies of periodic systems (e.g. crystals), particularly electrostatic energies. Ewald summation is a special case of the Poisson summation formula, replacing the summation of interaction energies in… …   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

  • Ramanujan summation — is a technique invented by the mathematician Srinivasa Ramanujan for assigning a sum to infinite divergent series. Although the Ramanujan summation of a divergent series is not a sum in the traditional sense, it has properties which make it… …   Wikipedia

  • Kahan summation algorithm — In numerical analysis, the Kahan summation algorithm (also known as compensated summation) significantly reduces the numerical error in the total obtained by adding a sequence of finite precision floating point numbers, compared to the obvious… …   Wikipedia

  • Poisson summation formula — The Poisson summation formula is an equation relating the coefficients of the Fourier Series of the periodic extension of a function in terms of the values of the function s continuous Fourier transform. The Poisson Summation Formula was… …   Wikipedia

  • Borel summation — In mathematics, a Borel summation is a generalisation of the usual notion of summation of a series. In particular it gives a definition of a quantity that in many ways behaves formally like the sum, even if the series is in fact… …   Wikipedia

  • Addition — is the mathematical process of putting things together. The plus sign + means that two numbers are added together. For example, in the picture on the right, there are 3 + 2 apples meaning three apples and two other apples which is the same as… …   Wikipedia

  • Hilbert space — For the Hilbert space filling curve, see Hilbert curve. Hilbert spaces can be used to study the harmonics of vibrating strings. The mathematical concept of a Hilbert space, named after David Hilbert, generalizes the notion of Euclidean space. It… …   Wikipedia

  • Coulomb's law — Electromagnetism Electricity · …   Wikipedia

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