Remarks on Some Integrals and Series Involving the Stirling Numbers and ζ(n)

From the perspective of the well-known identity Fin />•, • n r(C)T(c- a- b) 2Fx(a, b;c; 1) = —-———— —, 1 (c — a)X (c — b) we clarify the connections between the Stirling numbers s £ and the Riemann zeta function f(«). As a consequence, certain series and integrals can be evaluated in terms of £(n) and s £. 1.