On series arising from the approximation of periodic differentiable functions by Poisson integrals

被引：1

作者：

Zastavnyi, V. P. ^{[1
]}

机构：

[1] Donetsk Natl Univ, Donetsk, Ukraine

来源：

MATHEMATICAL NOTES | 2009年 / 86卷 / 3-4期

关键词：

periodic differentiable function; Poisson integral; Bernoulli polynomial; Euler polynomial; Stirling numbers; conformal mapping;

D O I：

10.1134/S0001434609090235

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：469 / 482

页数：14

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