Geodesic
On Series Arising from the Approximation of Periodic Differentiable Functions by Poisson Integrals
Matematičeskie zametki, Tome 86 (2009) no. 4, pp. 497-511

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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, Stirling numbers, conformal mapping.
Mots-clés : Poisson integral, Bernoulli polynomial, Euler polynomial 
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     author = {V. P. Zastavnyi},
     title = {On {Series} {Arising} from the {Approximation} of {Periodic} {Differentiable} {Functions} by {Poisson} {Integrals}},
     journal = {Matemati\v{c}eskie zametki},
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V. P. Zastavnyi. On Series Arising from the Approximation of Periodic Differentiable Functions by Poisson Integrals. Matematičeskie zametki, Tome 86 (2009) no. 4, pp. 497-511. http://geodesic.mathdoc.fr/item/MZM_2009_86_4_a2/