This article is cited in 1 paper

Convergence rate estimate of sine and cosine series with $1/k^q$ coefficients

M. G. Magomed-Kasumov<sup>ab

a</sup> Daghestan Scientific Centre of Russian Academy of Sciences, Makhachkala
^b Vladikavkaz Scientific Centre of the Russian Academy of Sciences

Abstract: Exact order-of-magnitude estimates of convergence rate of sine and cosine series with coefficients $1/k^q$, $q>1$, are obtained. In case when $0 \le q \le 1$ growth rate exact order-of-magnitude estimates of partial sums of sine and cosine series are proven.

Keywords: sine series, cosine series, lower estimate, convergence rate, growth rate.

UDC: 517.521

Received: 22.03.2017
Revised: 31.03.2017
Accepted: 03.04.2017

DOI: 10.31029/demr.7.5