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Jensen Polynomial

Let f(x) be a real entire function of the form

f(x)=sum_(k=0)^inftygamma_k(x^k)/(k!),
(1)

where the gamma_ks are positive and satisfy Turán's inequalities

gamma_k^2-gamma_(k-1)gamma_(k+1)>=0
(2)

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; k)gamma_kt^k,
(3)

where (a; b) is a binomial coefficient.

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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.

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Jensen Polynomial

Cite this as:

Weisstein, Eric W. "Jensen Polynomial." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/JensenPolynomial.html

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