In a recent work, Dancs and He found an Euler-type formula for
ζ(2n+1), n being a positive integer, which contains a series
they could not reduce to a finite closed-form. This open problem reveals a
greater complexity in comparison to ζ(2n), which is a rational multiple
of π2n. For the Dirichlet beta function, the things are `inverse':
β(2n+1) is a rational multiple of π2n+1 and no closed-form
expression is known for β(2n). Here in this work, I modify the Dancs-He
approach in order to derive an Euler-type formula for β(2n),
including β(2)=G, the Catalan's constant. I also convert the
resulting series into zeta series, which yields new exact closed-form
expressions for a class of zeta series involving β(2n) and a finite
number of odd zeta values. A closed-form expression for a certain zeta series
is also conjectured.Comment: 11 pages, no figures. A few small corrections. ACCEPTED for
publication in: Integral Transf. Special Functions (09/11/2011