  Euler discovered a formula for expressing the value of the Riemann zeta
function for all even positive integer arguments. A closed-form expression for
the Riemann zeta function for all odd integer arguments, based on the values of
the Dirichlet beta function, euler numbers and pi, reveals a new evidence about
the self-recursive nature of Riemann zeta function at odd integers. We
demonstrate for the first time that the Riemann zeta function at odd integers
always produces a recurrence relation that is self-recursive.
