A New Formula for The Values of Dirichlet Beta Function at Odd Positive Integers Based on The WZ Method

Abstract

By using the related results in the WZ theory, a new (as far as I know) formula for the values of Dirichlet beta function $\beta (s)=\sum _{n=1}^{+\infty }\frac{(-1{)}^{n-1}}{(2n-1{)}^s}$ (where $Re(s)>0$) at odd positive integers was given.

13 pages

References in corpus (1)

• Evaluations for zeta(2),zeta(4),...,zeta(2k)based on the WZ method