Lithuanian Mathematical Journal

, Volume 36, Issue 1, pp 58–67 | Cite as

The Euler-Maclaurin formula for functions with singularities

  • B. A. Kryžiené
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Abstract

Asymptotic formulas of the Euler-Maclaurin type are proved for the sum
$$\frac{1}{n}\sum\limits_{k = 1}^{n - 1} {\Phi \left( {\tfrac{k}{n}} \right) as n \to \infty .} $$
Here Φ(χ) is a sufficiently smooth function on the interval (0,1) and has singularities at the end points χ=0 and χ=1.

Keywords

Asymptotic Expansion Analytic Continuation Asymptotic Formula Bernoulli Number Bernoulli Polynomial 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Copyright information

© Plenum Publishing Corporation 1996

Authors and Affiliations

  • B. A. Kryžiené

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