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  2. Euler–Maclaurin formula - Wikipedia

    en.wikipedia.org/wiki/Euler–Maclaurin_formula

    The remainder term arises because the integral is usually not exactly equal to the sum. The formula may be derived by applying repeated integration by parts to successive intervals [r, r + 1] for r = m, m + 1, …, n − 1. The boundary terms in these integrations lead to the main terms of the formula, and the leftover integrals form the ...

  3. Summation by parts - Wikipedia

    en.wikipedia.org/wiki/Summation_by_parts

    The formula for an integration by parts is () ′ = [() ()] ′ (). Beside the boundary conditions , we notice that the first integral contains two multiplied functions, one which is integrated in the final integral ( g ′ {\displaystyle g'} becomes g {\displaystyle g} ) and one which is differentiated ( f {\displaystyle f} becomes f ...

  4. Cantor (mathematics software) - Wikipedia

    en.wikipedia.org/wiki/Cantor_(mathematics_software)

    Typesetting of mathematical formulas using LaTeX; Backend-aware syntax highlighting; Plugin-based assistant dialogs for common tasks (like integrating a function or entering a matrix) Cantor was the first KDE project to implement upload to the GetHotNewStuff addon service, which is used to download or upload example worksheets. It provided ...

  5. Integration by reduction formulae - Wikipedia

    en.wikipedia.org/wiki/Integration_by_reduction...

    The main idea is to express an integral involving an integer parameter (e.g. power) of a function, represented by I n, in terms of an integral that involves a lower value of the parameter (lower power) of that function, for example I n-1 or I n-2. This makes the reduction formula a type of recurrence relation. In other words, the reduction ...

  6. Riemann sum - Wikipedia

    en.wikipedia.org/wiki/Riemann_sum

    In mathematics, a Riemann sum is a certain kind of approximation of an integral by a finite sum. It is named after nineteenth century German mathematician Bernhard Riemann . One very common application is in numerical integration , i.e., approximating the area of functions or lines on a graph, where it is also known as the rectangle rule .

  7. Multiple zeta function - Wikipedia

    en.wikipedia.org/wiki/Multiple_zeta_function

    This sum conjecture is also known as Sum Theorem, and it may be expressed as follows: the Riemann zeta value of an integer n ≥ 2 is equal to the sum of all the valid (i.e. with s 1 > 1) MZVs of the partitions of length k and weight n, with 1 ≤ k ≤ n − 1. In formula: [3]

  8. Indefinite sum - Wikipedia

    en.wikipedia.org/wiki/Indefinite_sum

    The Laplace summation formula allows the indefinite sum to be written as the indefinite integral plus correction terms obtained from iterating the difference operator, although it was originally developed for the reverse process of writing an integral as an indefinite sum plus correction terms.

  9. Discrete calculus - Wikipedia

    en.wikipedia.org/wiki/Discrete_calculus

    Discrete integral calculus is the study of the definitions, properties, and applications of the Riemann sums. The process of finding the value of a sum is called integration . In technical language, integral calculus studies a certain linear operator .

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