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Matematicheskie Zametki, 2009, Volume 86, Issue 4, Pages 497–511
DOI: https://doi.org/10.4213/mzm5182 (Mi mzm5182) 		 
This article is cited in 2 scientific papers (total in 2 papers)

On Series Arising from the Approximation of Periodic Differentiable Functions by Poisson Integrals

V. P. Zastavnyi

Donetsk National University
Full-text PDF (485 kB) Citations (2)
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DOI: https://doi.org/10.4213/mzm5182
Abstract: For series of special form, we obtain an expansion in powers of the parameter. The coefficients of the expansion can be written out explicitly in terms of Bernoulli polynomials. In a particular case, we obtain an expansion in powers of the parameter of upper bounds for deviations of periodic differentiable functions from their Poisson integrals.
Keywords: periodic differentiable function, Poisson integral, Bernoulli polynomial, Euler polynomial, Stirling numbers, conformal mapping.
Received: 10.06.2008
Revised: 24.12.2008
English version:
Mathematical Notes, 2009, Volume 86, Issue 4, Pages 469–482
DOI: https://doi.org/10.1134/S0001434609090235
Bibliographic databases:
UDC: 517.518.83+517.521
Language: Russian
Citation: V. P. Zastavnyi, “On Series Arising from the Approximation of Periodic Differentiable Functions by Poisson Integrals”, Mat. Zametki, 86:4 (2009), 497–511; Math. Notes, 86:4 (2009), 469–482
Citation in format AMSBIB
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  • https://doi.org/10.4213/mzm5182
  • https://www.mathnet.ru/eng/mzm/v86/i4/p497
    • This publication is cited in the following 2 articles:
    1. V. P. Zastavnyi, V. V. Savchuk, “Approximation of Classes of Convolutions by Linear Operators of Special Form”, Math. Notes, 90:3 (2011), 333–343  mathnet  crossref  crossref  mathscinet  isi
    2. Viktor P. Zastavnyi, “Exact estimation of an approximation of some classes of differentiable functions by convolution operators”, J Math Sci, 175:2 (2011), 192  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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