ON COMPLETE MONOTONICITY OF CERTAIN SPECIAL FUNCTIONS

Given an entire function f(z) that has only negative zeros, we shall prove that all the functions of type f((m)) (x)/f((n)) (x), m > n are completely monotonic. Examples of this type are given for Laguerre polynomials, ultraspherical polynomials, Jacobi polynomials, Stieltjes-Wigert polynomials, q-Laguerre polynomials, Askey-Wilson polynomials, Ramanujan function, q-exponential functions, q-Bessel functions, Euler's gamma function, Airy function, modified Bessel functions of the first and the second kind, and the confluent basic hypergeometric series.