Geodesic
Asymptotics of Series Arising from the Approximation of Periodic Functions by Riesz and Cesàro Means
Matematičeskie zametki, Tome 93 (2013) no. 1, pp. 45-55

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Asymptotic expansions in powers of $\delta$ as $\delta\to+\infty$ of the series $$ \sum_{k=0}^\infty(-1)^{(\beta+1)k}\frac{Q((\delta^\alpha-(ak+b)^\alpha)_+)}{(ak+b)^{r+1}}, $$ where $\beta\in\mathbb Z$, $\alpha,a,b>0$, and $r\in\mathbb C$, while $Q$ is an algebraic polynomial satisfying the condition $Q(0)=0$, are obtained. In special cases, these series arise from the approximation of periodic differentiable functions by the Riesz and Cesàro means.
Keywords: Riesz mean, periodic differentiable function, approximation of periodic functions, Hurwitz function, Euler gamma function
Mots-clés : Cesàro mean, algebraic polynomial, Bernoulli spline, Euler spline, Bernoulli polynomial. 
V. P. Zastavnyi. Asymptotics of Series Arising from the Approximation of Periodic Functions by Riesz and Cesàro Means. Matematičeskie zametki, Tome 93 (2013) no. 1, pp. 45-55. http://geodesic.mathdoc.fr/item/MZM_2013_93_1_a3/
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