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Zeros of Bernoulli, generalized Bernoulli and Euler polynomials. (English) Zbl 0645.10015
Author’s abstract: “It is shown that the Bernoulli polynomials ${B}_{n}\left(z\right)$, the Euler polynomials ${E}_{n}\left(z\right)$ and the generalized Bernoulli polynomials ${B}_{\chi }^{n}\left(z\right)$ associated with certain quadratic characters have no zero inside a parabolic region if n is sufficiently large. Zero-free regions are also found for individual polynomials, and for the partial sums of sine and cosine. The proofs are based on a result on the maximum modulus of the zeros of polynomials related to the ${B}_{n}\left(z\right)$, ${E}_{n}\left(z\right)$ and ${B}_{\chi }^{n}\left(z\right)$. Finally, the distribution of the real zeros of ${B}_{\ell }^{n}\left(z\right)$ and ${E}_{n}\left(z\right)$ is studied. The results are similar to the known results on the real zeros of ${B}_{n}\left(z\right)$.”
Reviewer: L.Skula
##### MSC:
 11B39 Fibonacci and Lucas numbers, etc.