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  2. Cesàro summation - Wikipedia

    en.wikipedia.org/wiki/Cesàro_summation

    In mathematical analysis, Cesàro summation (also known as the Cesàro mean [1] [2] or Cesàro limit [3]) assigns values to some infinite sums that are not necessarily convergent in the usual sense. The Cesàro sum is defined as the limit, as n tends to infinity, of the sequence of arithmetic means of the first n partial sums of the series.

  3. Summation - Wikipedia

    en.wikipedia.org/wiki/Summation

    In mathematics, summation is the addition of a sequence of numbers, called addends or summands; the result is their sum or total.Beside numbers, other types of values can be summed as well: functions, vectors, matrices, polynomials and, in general, elements of any type of mathematical objects on which an operation denoted "+" is defined.

  4. Average - Wikipedia

    en.wikipedia.org/wiki/Average

    Average of chords. In ordinary language, an average is a single number or value that best represents a set of data. The type of average taken as most typically representative of a list of numbers is the arithmetic mean – the sum of the numbers divided by how many numbers are in the list. For example, the mean average of the numbers 2, 3, 4, 7 ...

  5. Summation of Grandi's series - Wikipedia

    en.wikipedia.org/wiki/Summation_of_Grandi's_series

    The basic idea is similar to Leibniz's probabilistic approach: essentially, the Cesàro sum of a series is the average of all of its partial sums. Formally one computes, for each n, the average σ n of the first n partial sums, and takes the limit of these Cesàro means as n goes to infinity. For Grandi's series, the sequence of arithmetic means is

  6. Arithmetic mean - Wikipedia

    en.wikipedia.org/wiki/Arithmetic_mean

    In mathematics and statistics, the arithmetic mean (/ ˌ æ r ɪ θ ˈ m ɛ t ɪ k / arr-ith-MET-ik), arithmetic average, or just the mean or average (when the context is clear) is the sum of a collection of numbers divided by the count of numbers in the collection. [1] The collection is often a set of results from an experiment, an ...

  7. Summation by parts - Wikipedia

    en.wikipedia.org/wiki/Summation_by_parts

    In mathematics, summation by parts transforms the summation of products of sequences into other summations, often simplifying the computation or (especially) estimation of certain types of sums. It is also called Abel's lemma or Abel transformation , named after Niels Henrik Abel who introduced it in 1826.

  8. Sums of powers - Wikipedia

    en.wikipedia.org/wiki/Sums_of_powers

    In mathematics and statistics, sums of powers occur in a number of contexts: . Sums of squares arise in many contexts. For example, in geometry, the Pythagorean theorem involves the sum of two squares; in number theory, there are Legendre's three-square theorem and Jacobi's four-square theorem; and in statistics, the analysis of variance involves summing the squares of quantities.

  9. Weight function - Wikipedia

    en.wikipedia.org/wiki/Weight_function

    A weight function is a mathematical device used when performing a sum, integral, or average to give some elements more "weight" or influence on the result than other elements in the same set. The result of this application of a weight function is a weighted sum or weighted average .