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Euler's Summation Formula

  • Definition: Euler's summation formula relates the integral of a function over an interval [a, b] with the sum of the function values at the integers in [a, b]. It can sometimes be used to approximate integrals by sums or, conversely, to estimate the values of certain sums by means of integrals.

    Source: Mathematical Analysis, second edition by Tom M. Apostol

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