Recently, K. I. Gross and the author [ J. Approx. Theory 59:224–246 (1989)] analyzed the total positivity of kernels of the form K(x,y) = p F q(xy) , x, y ϵ R, where p F q denotes a classical generalized hypergeometric series. There, we related the determinants which define the total positivity of K to the hypergeometric functions of matrix argument, defined on the space of n × n Hermitian matrices. In the first part of this paper, we apply these methods to derive the total positivity properties of the kernels K for more general choices of the parameters in these hypergeometric series. In particular, we prove that if a i > 0 and k i is a positive integer ( i = 1,…, p) then K(x,y) = p F q(a 1,…,a p;a 1 + k 1,…,a p + k p; xy) is strictly totally positive on R 2. In the second part, we use the theory of entire functions to derive some Pólya frequency function properties of the hypergeometric series p F q ( x). Some of these latter results suggest a curious duality with the total positivity properties described above. For instance, we prove that if p > 1 and the a i and k i are as above, then there exists a probability density function f on R, such that f is a strict Pólya frequency function, and 1/ p F p(a 1+k 1,…,a p+k p;a 1,…,a p;z= Lf(z) , the Laplace transform of f.