Jensen polynomials for the Riemann xi-function

We investigate Riemann's xi function $\xi(s):=\frac{1}{2}s(s-1)\pi^{-\frac{s}{2}}\Gamma(\frac{s}{2})\zeta(s)$ (here $\zeta(s)$ is the Riemann zeta function). The Hypothesis (RH) asserts that if $\xi(s)=0$, then $\mathrm{Re}(s)=\frac{1}{2}$. P\'olya proved RH equivalent to hyperbolicity of Jensen polynomials $J^{d,n}(X)$ constructed from certain Taylor coefficients $\xi(s)$. For each $d\geq 1$, recent work proves hyperbolic for sufficiently large $n$. Here we make this result effective. Moreover, show how low-lying zeros derivatives $\xi^{(n)}(s)$ influence $J^{d,n}(X)$.