This article is cited in 2 papers

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

V. P. Zastavnyi

Donetsk National University

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.

UDC: 517.518.83+517.521

Received: 10.06.2008
Revised: 24.12.2008

DOI: 10.4213/mzm5182

 English version: Mathematical Notes, 2009, 86:4, 469–482

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