  In this article, we derive an expression for the complex magnitude of the
Dirichlet beta function $\beta(s)$ represented as a Euler prime product and
compare with similar results for the Riemann zeta function. We also obtain
formulas for $\beta(s)$ valid for an even and odd $k$th positive integer
argument and present a set of generated formulas for $\beta(k)$ up to $11$th
order, including Catalan's constant and compute these formulas numerically.
Additionally, we derive a second expression for the complex magnitude of
$\beta(s)$ valid in the critical strip from which we obtain a formula for the
Euler-Mascheroni constant expressed in terms of zeros of the Dirichlet beta
function on the critical line. Finally, we investigate the asymptotic behavior
of the Euler prime product on the critical line.
