Log-convexity and log-concavity for series in gamma ratios and applications

S. I. Kalmykov, D. B. Karp

Polynomial sequence ${P_m}_{m\ge 0}$ is $q$-logarithmically concave if $P_m^2-P_{m+1}{P}_{m-1}$ is a polynomial with nonnegative coefficients for any $m\ge 1$. We introduce an an…