Let
be a real entire function of
the form
![f(x)=sum_(k=0)^inftygamma_k(x^k)/(k!),](/images/equations/JensenPolynomial/NumberedEquation1.svg) |
(1)
|
where the
s
are positive and satisfy Turán's
inequalities
![gamma_k^2-gamma_(k-1)gamma_(k+1)>=0](/images/equations/JensenPolynomial/NumberedEquation2.svg) |
(2)
|
for
,
2, .... The Jensen polynomial
associated with
is then given by
![g_n(t)=sum_(k=0)^n(n; k)gamma_kt^k,](/images/equations/JensenPolynomial/NumberedEquation3.svg) |
(3)
|
where
is a binomial coefficient.
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References
Csordas, G.; Varga, R. S.; and Vincze, I. "Jensen Polynomials with Applications to the Riemann
-Function." J. Math. Anal. Appl. 153,
112-135, 1990.Referenced on Wolfram|Alpha
Jensen Polynomial
Cite this as:
Weisstein, Eric W. "Jensen Polynomial."
From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/JensenPolynomial.html
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