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 Citations (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.}}

Original language	English
Journal	Analysis and Applications
Volume	9
Issue number	4
Pages (from-to)	409-419
ISSN	0219-5305
DOIs	https://doi.org/10.1142/S0219530511001911
Publication status	Published - Oct 2011

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10.1142/S0219530511001911

Cite this

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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

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EP - 419

JO - Analysis and Applications

JF - Analysis and Applications

IS - 4

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