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

Stamatis Koumandos; Henrik Laurberg Pedersen

doi:10.1002/mana.201100299

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

Stamatis Koumandos, Henrik Laurberg Pedersen

Department of Mathematical Sciences

8 Citations (Scopus)

Abstract

Turán 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 Turán inequalities of partial sums with Turán inequalities of the corresponding remainders in any Maclaurin expansion. Remainders in asymptotic expansions of the β-function are shown to be completely monotonic of positive order.

Original language	English
Journal	Mathematische Nachrichten
Volume	285
Issue number	17-18
Pages (from-to)	2129-2156
ISSN	0025-584X
DOIs	https://doi.org/10.1002/mana.201100299
Publication status	Published - Dec 2012

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title = "Tur{\'a}n type inequalities for the partial sums of the generating functions of Bernoulli and Euler numbers",

abstract = "Tur{\'a}n 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 Tur{\'a}n inequalities of partial sums with Tur{\'a}n inequalities of the corresponding remainders in any Maclaurin expansion. Remainders in asymptotic expansions of the β-function are shown to be completely monotonic of positive order.",

author = "Stamatis Koumandos and Pedersen, {Henrik Laurberg}",

year = "2012",

month = dec,

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number = "17-18",

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T1 - Turán type inequalities for the partial sums of the generating functions of Bernoulli and Euler numbers

AU - Koumandos, Stamatis

AU - Pedersen, Henrik Laurberg

PY - 2012/12

Y1 - 2012/12

N2 - Turán 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 Turán inequalities of partial sums with Turán inequalities of the corresponding remainders in any Maclaurin expansion. Remainders in asymptotic expansions of the β-function are shown to be completely monotonic of positive order.

AB - Turán 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 Turán inequalities of partial sums with Turán inequalities of the corresponding remainders in any Maclaurin expansion. Remainders in asymptotic expansions of the β-function are shown to be completely monotonic of positive order.

U2 - 10.1002/mana.201100299

DO - 10.1002/mana.201100299

M3 - Journal article

SN - 0025-584X

VL - 285

SP - 2129

EP - 2156

JO - Mathematische Nachrichten

JF - Mathematische Nachrichten

IS - 17-18

ER -