Absolutely monotonic functions related to Euler's gamma function and Barnes' double and triple gamma function

Stamatis Koumandos; Henrik Laurberg Pedersen

doi:10.1007/s00605-010-0197-9

Absolutely monotonic functions related to Euler's gamma function and Barnes' double and triple gamma function

Stamatis Koumandos, Henrik Laurberg Pedersen

9 Citations (Scopus)

Abstract

It is shown that the remainders in asymptotic expansions of the logarithm of Barnes double and triple gamma function and Euler's gamma function are Laplace transformations of positive multiples of absolutely monotonic functions. Applications concerning positivity of sums involving Bernoulli numbers are given.

Original language	English
Journal	Monatshefte für Mathematik
Volume	163
Issue number	1
Pages (from-to)	51-69
Number of pages	19
ISSN	0026-9255
DOIs	https://doi.org/10.1007/s00605-010-0197-9
Publication status	Published - May 2011

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abstract = "It is shown that the remainders in asymptotic expansions of the logarithm of Barnes double and triple gamma function and Euler's gamma function are Laplace transformations of positive multiples of absolutely monotonic functions. Applications concerning positivity of sums involving Bernoulli numbers are given.",

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AU - Pedersen, Henrik Laurberg

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N2 - It is shown that the remainders in asymptotic expansions of the logarithm of Barnes double and triple gamma function and Euler's gamma function are Laplace transformations of positive multiples of absolutely monotonic functions. Applications concerning positivity of sums involving Bernoulli numbers are given.

AB - It is shown that the remainders in asymptotic expansions of the logarithm of Barnes double and triple gamma function and Euler's gamma function are Laplace transformations of positive multiples of absolutely monotonic functions. Applications concerning positivity of sums involving Bernoulli numbers are given.

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DO - 10.1007/s00605-010-0197-9

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EP - 69

JO - Monatshefte für Mathematik

JF - Monatshefte für Mathematik

IS - 1

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Absolutely monotonic functions related to Euler's gamma function and Barnes' double and triple gamma function

Abstract

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