## Experimental Mathematics

- Experiment. Math.
- Volume 9, Issue 1 (2000), 3-12.

### Convergence acceleration of alternating series

Henri Cohen, Fernando Rodriguez Villegas, and Don Zagier

#### Abstract

We discuss some linear acceleration methods for alternating series which are in theory and in practice much better than that of Euler--Van Wijngaarden. One of the algorithms, for instance, allows one to calculate $\sum(-1)^ka_k$ with an error of about $17$.$93^{-n}$ from the first $n$ terms for a wide class of sequences $\{a_k\}$. Such methods are useful for high precision calculations frequently appearing in number theory.

#### Article information

**Source**

Experiment. Math., Volume 9, Issue 1 (2000), 3-12.

**Dates**

First available in Project Euclid: 5 March 2003

**Permanent link to this document**

https://projecteuclid.org/euclid.em/1046889587

**Mathematical Reviews number (MathSciNet)**

MR1758796

**Zentralblatt MATH identifier**

0972.11115

**Subjects**

Primary: 11Y55: Calculation of integer sequences

Secondary: 65B05: Extrapolation to the limit, deferred corrections

**Keywords**

Convergence acceleration alternating sum Chebyshev polynomial

#### Citation

Cohen, Henri; Rodriguez Villegas, Fernando; Zagier, Don. Convergence acceleration of alternating series. Experiment. Math. 9 (2000), no. 1, 3--12. https://projecteuclid.org/euclid.em/1046889587