Turan type inequalities for the partial sums of the generating functions of Bernoulli and Euler numbers

被引：8

作者：

Koumandos, Stamatis ^{[2
]}

Pedersen, Henrik Laurberg ^{[1
]}

机构：

[1] Univ Copenhagen, Dept Math Sci, DK-2100 Copenhagen, Denmark

[2] Univ Cyprus, Dept Math & Stat, CY-1678 Nicosia, Cyprus

来源：

MATHEMATISCHE NACHRICHTEN | 2012年 / 285卷 / 17-18期

关键词：

Turan inequality; Bernoulli numbers; Euler numbers; generating functions; remainders in asymptotic expansions; completely monotonic functions of positive order; ratio of series of functions; beta-function; MONOTONIC FUNCTIONS; ASYMPTOTIC EXPANSIONS; ORDER; SEQUENCES; LOGARITHM;

D O I：

10.1002/mana.201100299

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Turan type inequalities for the partial sums of the generating functions of the Bernoulli and Euler numbers are established. They are shown to follow from a general result relating Turan inequalities of partial sums with Turan inequalities of the corresponding remainders in any Maclaurin expansion. Remainders in asymptotic expansions of the beta-function are shown to be completely monotonic of positive order. (C) 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

引用

页码：2129 / 2156

页数：28

共 31 条

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