Uniform Convergence Behavior of the Bernoulli Polynomials
نویسنده
چکیده
The roots of Bernoulli polynomials, Bn(z), when plotted in the complex plane, accumulate around a peculiar H-shaped curve. Karl Dilcher proved in 1987 that, on compact subsets of C, the Bernoulli polynomials asymptotically behave like sine or cosine. Here we establish the asmptotic behavior of Bn(nz), compute the distribution of real roots of Bernoulli polynomials and show that, properly rescaled, the complex roots lie on the curve e = 2πe|z| or e = 2πe|z|.
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