### 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.