Complete Bernstein functions and scaled ultraspherical zeros

Let $z_{n,j}(λ)$ denote the positive zeros, in decreasing order, of the ultraspherical polynomial $C_n^λ$, $λ>-1/2$, with the reduced limiting interpretation at $λ=0$ specified below. Our principal result settles three higher-monotonicity questions of Gautschi: two as printed and the natural open-in