Given an entire function
f
(
z
)
f(z)
that has only negative zeros, we shall prove that all the functions of type
f
(
m
)
(
x
)
/
f
(
n
)
(
x
)
,
m
>
n
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
q
-Laguerre polynomials, Askey-Wilson polynomials, Ramanujan function,
q
q
-exponential functions,
q
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.