Turán's Inequalities

For a set of Positive $\gamma_k$, $k=0$, 1, 2..., Turán's inequalities are given by

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

for $k=1$, 2, ....

See also Jensen Polynomial

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.

Szegö, G. Orthogonal Polynomials, 4th ed. Providence, RI: Amer. Math. Soc., p. 388, 1975.