Dirichlet's eta and beta functions: Concavity and fast computation of their derivatives

被引：14

作者：

Adell, Jose A. ^{[1
]}

Lekuona, Alberto ^{[1
]}

机构：

[1] Univ Zaragoza, Fac Ciencias, Dept Metodos Estadist, E-50009 Zaragoza, Spain

来源：

JOURNAL OF NUMBER THEORY | 2015年 / 157卷

关键词：

Dirichlet's eta function; Dirichlet's beta function; Concavity; Fast computation; Gamma process; DOUBLE INTEGRALS;

D O I：

10.1016/j.jnt.2015.05.006

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

For any a is an element of (0, infinity), we prove the strict concavity of the function eta(a)(t) := Sigma(infinity)(m=0) (-1)(m)/(am+1)(t) on (0, infinity), and provide fast computations of their derivatives on (0, infinity). We give short proofs mainly based on differentiation formulas concerning the gamma process. In particular, our results apply to Dirichlet's eta and beta functions eta(1)(t) and eta(2)(t), respectively. (C) 2015 Elsevier Inc. All rights reserved.

引用

页码：215 / 222

页数：8

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