REMARKS ON A SUM INVOLVING BINOMIAL COEFFICIENTS

Let S-p(a, b; t) = 1/b Sigma(p)(k=0) ((p)(k))/((ak+b)(b))t(k), with p is an element of N, 0 < a is an element of R, 0 < b is an element of R, t is an element of R. We prove that S-p(a , b; t) is completely monotonic on (0, infinity) as a function of a (if t > 0) and as a function of b (if t >=-1) . This extends a result of Sofo, who proved that a bar right arrow S-p (a , b; t) is strictly decreasing, convex, and log-convex on [1, infinity).