Logarithmic concavity of series in gamma ratios (Q2262902)

The authors consider power series of the form \(g_{a,c} (\mu ;x)=\sum _{n=0}^{\infty }g_{n} \frac{\Gamma (a+\mu +n)}{\Gamma (c+\mu +n)} x^{n} \) , where \(g_{n} \geq 0,\; n=0,1,\ldots\) Conditions on the sequence \(g_{n} \) and on the constants \(a,c\) are imposed ensuring that the function \(\mu \to g_{a,c} (\mu ;x)\) is logarithmically concave.