Fundamental relations between the Dirichlet beta function, euler\n numbers, and Riemann zeta function for positive integers

A new definition for the Dirichlet beta function for positive integer\narguments is discovered and presented for the first time. This redefinition of\nthe Dirichlet beta function, based on the polygamma function for some special\nvalues, provides a general method for obtaining all special constants\nassociated with Dirichlet beta function. We also show various new and\nfundamental relations between the polygamma function, Riemann zeta, the\neven-indexed euler numbers, the Dirichlet beta functions in a way never seen or\nimagined before.\n