  We find an inverse factorial series expansion for the ratio of products of
gamma functions whose arguments are linear functions of the variable. We a give
recurrence relation for the coefficients in terms of the N{\o}rlund-Bernoulli
polynomials and determine quite precisely the half-plane of convergence. Our
results complement naturally a number of previous investigations of the gamma
ratios which began in the 1930ies. The expansion obtained in this paper plays a
crucial role in the study of the behavior of the delta-neutral Fox's H function
in the neighborhood of it's finite singular point. We further apply a
particular case of the inverse factorial series expansion to derive a possibly
new identity for the N{\o}rlund-Bernoulli polynomials.
