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

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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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Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, The University of Cyprus, P. O. Box 20537, 1678, Nicosia, Cyprus

    Stamatis Koumandos

  2. Department of Basic Sciences and Environment, Mathematics and Computer Science, Faculty of Life Sciences, University of Copenhagen, 40, Thorvaldsensvej, 1871, Frederiksberg C, Denmark

    Henrik L. Pedersen

Authors
  1. Stamatis Koumandos
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  2. Henrik L. Pedersen
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Corresponding author

Correspondence to Henrik L. Pedersen.

Additional information

S. Koumandos acknowledges support by Grant number 3411-21041 from the Leventis Foundation.

H. L. Pedersen acknowledges support by Grant 272-07-0321 from the Danish Research Council for Nature and Universe.

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Koumandos, S., Pedersen, H.L. Absolutely monotonic functions related to Euler’s gamma function and Barnes’ double and triple gamma function. Monatsh Math 163, 51–69 (2011). https://doi.org/10.1007/s00605-010-0197-9

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  • DOI: https://doi.org/10.1007/s00605-010-0197-9

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