Error estimates for the Gregory-Leibniz series and the alternating harmonic series using Dalzell integrals

Abstract

The computation of Dalzell integrals ${\int }_0^1\frac{x^m(1-x{)}^n}{1+x^2}dx>0$ gives new error estimates for the partial sums of the Gregory-Leibniz series $1-\frac{1}{3}+\frac{1}{5}-\frac{1}{7}\pm \dots$ and for the alternating harmonic series $1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}\pm \dots$

7 pages