Abstract:
A new method for accelerating the convergence of trigonometric series for decreasing on infinity functions is proposed. The key idea is to replace the original series with a weighted sum involving a specially designed weight function. The computation is based on Cauchy's theorem with a carefully chosen integration contour, ensuring exponential convergence. As a consequence, summation formulas for linear argument transformations and sums with periodic multiplier are derived.
Key words and phrases:Sum of series, trigonometric series, convergence acceleration, special functions, zeta-functions.
Fulltext:
PDF file (437 kB)