  By means of a variational approach we find new series representations both
for well known mathematical constants, such as $\pi$ and the Catalan constant,
and for mathematical functions, such as the Riemann zeta function. The series
that we have found are all exponentially convergent and provide quite useful
analytical approximations. With limited effort our method can be applied to
obtain similar exponentially convergent series for a large class of
mathematical functions.
