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# A pr 2 00 2 Discrete analogues of the Laguerre Inequality

@inproceedings{Krasikov2003AP2, title={A pr 2 00 2 Discrete analogues of the Laguerre Inequality}, author={Ilia Krasikov}, year={2003} }

- Published 2003

It is shown that ∑m j=−m(−1) f(x−j)(f(x+j) (m−j)!(m+j)! ≥ 0, m = 0, 1, ..., where f(x) is either a real polynomial with only real zeros or an allied entire function of a special type, provided the distance between two consecutive zeros of f(x) is at least √ 4 − 6 m+2 . These inequalities are a surprisingly similar discrete analogue of higher degree generalizations of the Laguerre and Turan inequalities. Being applied to the classical discrete orthogonal polynomials, they yield sharp, explicit… CONTINUE READING