Completely monotonic functions related to logarithmic derivatives of entire functions

Henrik Laurberg Pedersen

doi:10.1142/S0219530511001911

Completely monotonic functions related to logarithmic derivatives of entire functions

4 Citationer (Scopus)

Abstract

The logarithmic derivative l(x) of an entire function of genus p and having only non-positive zeros is represented in terms of a Stieltjes function. As a consequence, (-1)^{p(x^{ml(x))^(m+p)
is a completely monotonic function for all m ≥ 0. This generalizes
earlier results on complete monotonicity of functions related to Euler's
psi-function. Applications to Barnes' multiple gamma functions are
given.}}

Originalsprog	Engelsk
Tidsskrift	Analysis and Applications
Vol/bind	9
Udgave nummer	4
Sider (fra-til)	409-419
ISSN	0219-5305
DOI	https://doi.org/10.1142/S0219530511001911
Status	Udgivet - okt. 2011

Adgang til dokumentet

10.1142/S0219530511001911

Citationsformater

@article{3a54b9bb96dd4c079819a03fd0763224,

title = "Completely monotonic functions related to logarithmic derivatives of entire functions",

abstract = "The logarithmic derivative l(x) of an entire function of genus p and having only non-positive zeros is represented in terms of a Stieltjes function. As a consequence, (-1)p(xml(x))(m+p) is a completely monotonic function for all m ≥ 0. This generalizes earlier results on complete monotonicity of functions related to Euler's psi-function. Applications to Barnes' multiple gamma functions are given.",

author = "Pedersen, {Henrik Laurberg}",

year = "2011",

month = oct,

doi = "10.1142/S0219530511001911",

language = "English",

volume = "9",

pages = "409--419",

journal = "Analysis and Applications",

issn = "0219-5305",

publisher = "World Scientific Publishing Co. Pte. Ltd.",

number = "4",

}

TY - JOUR

T1 - Completely monotonic functions related to logarithmic derivatives of entire functions

AU - Pedersen, Henrik Laurberg

PY - 2011/10

Y1 - 2011/10

N2 - The logarithmic derivative l(x) of an entire function of genus p and having only non-positive zeros is represented in terms of a Stieltjes function. As a consequence, (-1)p(xml(x))(m+p) is a completely monotonic function for all m ≥ 0. This generalizes earlier results on complete monotonicity of functions related to Euler's psi-function. Applications to Barnes' multiple gamma functions are given.

AB - The logarithmic derivative l(x) of an entire function of genus p and having only non-positive zeros is represented in terms of a Stieltjes function. As a consequence, (-1)p(xml(x))(m+p) is a completely monotonic function for all m ≥ 0. This generalizes earlier results on complete monotonicity of functions related to Euler's psi-function. Applications to Barnes' multiple gamma functions are given.

U2 - 10.1142/S0219530511001911

DO - 10.1142/S0219530511001911

M3 - Journal article

SN - 0219-5305

VL - 9

SP - 409

EP - 419

JO - Analysis and Applications

JF - Analysis and Applications

IS - 4

ER -