  In this paper we present a method for computing the total probability
corresponding to the processes of fermion pair production in dipole magnetic
field and external Coulomb field in a de Sitter geometry. For that we rewrite
the functions that define the amplitudes in terms of oscillatory functions and
we use the Taylor expansion of these functions for arriving at the final form
of the momenta integrals. The total probability is analysed in terms of the
ratio between the mass of the fermion and expansion parameter and we recover
the Minkowski limit when the expansion parameter is vanishing. Finally it is
proven that from our results we can compute the number of fermions in terms of
expansion parameter.
