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

共 31 条

[1] On series arising from the approximation of periodic differentiable functions by Poisson integrals
V. P. Zastavnyi
Mathematical Notes, 2009, 86
[2] Approximation of differentiable periodic functions by their biharmonic Poisson integrals
Zhyhallo K.M.
Kharkevych Yu.I.
Ukrainian Mathematical Journal, 2002, 54 (9) : 1462 - 1470
[3] Asymptotics of series arising from the approximation of periodic functions by Riesz and Cesàro means
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Mathematical Notes, 2013, 93 : 58 - 68
[4] Asymptotics of series arising from the approximation of periodic functions by Riesz and CesA ro means
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[5] ASYMPTOTICS OF APPROXIMATION OF FUNCTIONS BY CONJUGATE POISSON INTEGRALS
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[6] Asymptotics of approximation of conjugate functions by Poisson integrals
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[7] Complete asymptotics of the deviation of a class of differentiable functions from the set of their harmonic poisson integrals
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[8] On the approximation of functions of the Holder class by biharmonic Poisson integrals
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Ukrainian Mathematical Journal, 2000, 52 (7) : 1113 - 1117
[9] On the approximation of functions of the holder class by triharmonic poisson integrals
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Ukrainian Mathematical Journal, 2001, 53 (6) : 1012 - 1018
[10] Complete asymptotics of the approximation of function from the Sobolev classes by the Poisson integrals
Kal'chuk, I. V.
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ACTA ET COMMENTATIONES UNIVERSITATIS TARTUENSIS DE MATHEMATICA, 2018, 22 (01): : 23 - 36

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