Some theorems on stirling-type pairs

Abstract

It is shown that an extended Schlomilch formula for Stirling-type pairs of numbers and the inversion formula of Lagrange are implied by each other. Also proved are some congruence relations modulo a prime number p(>2) associated with generalized Stirling numbers. The third result in concerned with the asymptotic expansions of Stirling-type pairs involving large parameters. © 1993, Edinburgh Mathematical Society. All rights reserved.