  In this paper, we show that the price of an European call option, whose
underlying asset price is driven by the space-time fractional diffusion, can be
expressed in terms of rapidly convergent double-series. The series formula can
be obtained from the Mellin-Barnes representation of the option price with help
of residue summation in $\mathbb{C}^2$. We also derive the series
representation for the associated risk-neutral factors, obtained by Esscher
transform of the space-time fractional Green functions.
