Approximation theory
Daghestan Electronic Mathematical Reports: Issue 7 (2017)
Convergence rate estimate of sine and cosine series with $1/k^q$ coefficients
UDK: 517.521
Pages: 47 - 51
DOI: 10.31029/demr.7.5
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.