Hausdorff moment sequences and hypergeometric functions
Hausdorff moment sequences and hypergeometric functions
P\'olya in 1926 showed that the hypergeometric function $F(z)=\null_2F_1(a,b;c;z)$ has a totally monotone sequence as its coefficients; that is, $F$ is the generating function of a Hausdorff moment sequence, when $0\le a\le 1$ and $0\le b\le c.$ In this paper, we give a complete characterization of such hypergeometric functions $F$ …