  A new definition for the Dirichlet beta function for positive integer
arguments is discovered and presented for the first time. This redefinition of
the Dirichlet beta function, based on the polygamma function for some special
values, provides a general method for obtaining all special constants
associated with Dirichlet beta function. We also show various new and
fundamental relations between the polygamma function, Riemann zeta, the
even-indexed euler numbers, the Dirichlet beta functions in a way never seen or
imagined before.
