Abstract: MATH/CHEM/COMP 2002, Dubrovnik,
June 2429, 2002

Applying an Euler type transformation for accelerating convergence
of trigonometric series
Faton M. Berisha and Muharrem Q. Berisha Faculty of Mathematical and Natural Sciences, University of
Prishtina, Prishtina,Kosova
For a sequence of real or complex numbers _{} and a given sequence _{} the linear operator _{} is defined by _{} Theorem 1. Let _{} be a convergent real or complex trigonometric series and _{} a sequence of real or complex numbers such that _{}. Then the following equation holds true _{} (1) where are _{}. Corollary 1. If there exist the finite limits _{} _{}, then series on the lefthand side of (1) converges faster then the series on the righthand side. The acceleration of convergence is increased with the value of p. Example 1. Let _{}. Then _{} Obviously, for every integer p the sequence _{} satisfies the conditions of Corollary 1. In particular, in order to calculate the approximate sum of the series _{} with an error not greater than _{} we must compute the sum of first 9 terms. Applying the transformation (1), the same accuracy is obtained by computing the sum of 5 terms for _{}, 3 terms for _{} and 1 term for _{}. 