Jensen Polynomial

Let $f(x)$ be a real Entire Function of the form

$$f(x)=\sum_{k=0}^\infty \gamma_k {x^k\over k!},$$

where the $\gamma_k$s are Positive and satisfy Turán's Inequalities

$${\gamma_k}^2-\gamma_{k-1}\gamma_{k+1}\geq 0$$

for $k=1$, 2, .... The Jensen polynomial $g(t)$ associated with $f(x)$ is then given by

$$g_n(t)=\sum_{k=0}^n{n\choose k}\gamma_k t^k,$$

where ${a\choose b}$ is a Binomial Coefficient.

References

Csordas, G.; Varga, R. S.; and Vincze, I. ``Jensen Polynomials with Applications to the Riemann $\zeta$-Function.'' J. Math. Anal. Appl. 153, 112-135, 1990.