Email this article Mean oscillation modulus and number-theoretic grid quadrature formulas
- Authors: Sevast’yanov E.A.1
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Affiliations:
- National Research Nuclear University “MIFI,”
- Issue: Vol 101, No 1-2 (2017)
- Pages: 320-340
- Section: Volume 101, Number 2, February, 2017
- URL: https://journals.rcsi.science/0001-4346/article/view/149996
- DOI: https://doi.org/10.1134/S0001434617010369
- ID: 149996
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Abstract
For arbitrary Riemann integrable functions f and irrational numbers θ ∈ (0, 1), we obtain estimates of the error Rn(f, θ) of the quadrature formula
\(\int_0^1 {f\left( x \right)dx = \frac{1}{n}\sum\limits_{k = 1}^n {f\left( {\left\{ {k\theta } \right\}} \right) - {R_n}\left( {f,\theta } \right)} } \)![]()
in which {kθ} is the fractional part of the number kθ.About the authors
E. A. Sevast’yanov
National Research Nuclear University “MIFI,”
Author for correspondence.
Email: sevastianov.e.a@mail.ru
Russian Federation, Moscow
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