ASYMPTOTIC ESTIMATES FOR APOSTOL-BERNOULLI AND APOSTOL-EULER POLYNOMIALS

作者：Navas Luis M^*; Ruiz Francisco J; Varona Juan L

来源：Mathematics of Computation, 2012, 81(279): 1707-1722.

DOI：10.1090/S0025-5718-2012-02568-3

• Apostol-Bernoulli polynomials
• Apostol-Euler polynomials
• Fourier series
• asymptotic estimates

We analyze the asymptotic behavior of the Apostol-Bernoulli polynomials B-n (x; lambda) in detail. The starting point is their Fourier series on [0, 1] which, it is shown, remains valid as an asymptotic expansion over compact subsets of the complex plane. This is used to determine explicit estimates on the constants in the approximation, and also to analyze oscillatory phenomena which arise in certain cases. %26lt;br%26gt;These results are transferred to the Apostol-Euler polynomials epsilon(n) (x; lambda) via a simple relation linking them to the Apostol-Bernoulli polynomials.

• 出版日期2012-7