Completely monotonic functions related to logarithmic derivatives of entire functions
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Completely monotonic functions related to logarithmic derivatives of entire functions. / Pedersen, Henrik Laurberg.
I: Analysis and Applications, Bind 9, Nr. 4, 2011, s. 409-419.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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TY - JOUR
T1 - Completely monotonic functions related to logarithmic derivatives of entire functions
AU - Pedersen, Henrik Laurberg
PY - 2011
Y1 - 2011
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
VL - 9
SP - 409
EP - 419
JO - Analysis and Applications
JF - Analysis and Applications
SN - 0219-5305
IS - 4
ER -
ID: 131444681