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We find an inverse factorial series expansion for the ratio of products ofgamma functions whose arguments are linear functions of the variable. We a giverecurrence relation for the coefficients in terms of the N{\o}rlund-Bernoullipolynomials and determine quite precisely the half-plane of convergence. Ourresults complement naturally a number of previous investigations of the gammaratios which began in the 1930ies. The expansion obtained in this paper plays acrucial role in the study of the behavior of the delta-neutral Fox's H functionin the neighborhood of it's finite singular point. We further apply aparticular case of the inverse factorial series expansion to derive a possiblynew identity for the N{\o}rlund-Bernoulli polynomials.

An inverse factorial series for a general gamma ratio and related properties of the N{\o}rlund-Bernoulli polynomials