ASYMPTOTIC ESTIMATES FOR APOSTOL-BERNOULLI AND APOSTOL-EULER POLYNOMIALS

被引：28
|
作者：
Navas, Luis M. [1 ]
Ruiz, Francisco J. [2 ]
Varona, Juan L. [3 ]
机构：
[1] Univ Salamanca, Dept Math, E-37008 Salamanca, Spain
[2] Univ Zaragoza, Dept Matemat, E-50009 Zaragoza, Spain
[3] Univ La Rioja, Dept Matemat & Computac, Logrono 26004, Spain
来源：
MATHEMATICS OF COMPUTATION | 2012年 / 81卷 / 279期
关键词：
Apostol-Bernoulli polynomials; Apostol-Euler polynomials; Fourier series; asymptotic estimates;
D O I：
10.1090/S0025-5718-2012-02568-3
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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. These results are transferred to the Apostol-Euler polynomials epsilon(n) (x; lambda) via a simple relation linking them to the Apostol-Bernoulli polynomials.
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页码：1707 / 1722
页数：16
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