  We introduce the technique of inverse Mellin transform in a problem of
strong-field QED. We show that the {\it moments} of pair production width in a
uniform background magnetic field are proportional to the derivatives of photon
polarization function at the zero momentum. Hence, the pair-production width or
the absorptive part of the photon polarization function is calculable from the
latter by the inverse Mellin transform. Using the {\it Kramers-Kronig}
relation, the dispersive part of photon polarization function can be computed
as well. Therefore the analytic property of the photon polarization function in
all energy range is obtained. We also discuss briefly the possible extensions
of this technique to other problems.
