Completely monotonic functions of positive order and asymptotic expansions of the logarithm of Barnes double gamma function and Euler's gamma function

Details Completely monotonic functions of positive order and asymptotic expansions of the logarithm of Barnes double gamma function and Euler's gamma function Completely monotonic functions of positive order and asymptotic expansions of the logarithm of Barnes double gamma function and Euler's gamma function

2008-11-18

arxiv.org/abs/0811.2870v2

Mathematics

Classical Analysis and ODEs

13 pages, to appear in Journal of Mathematical Analysis and Applications

Scientific paper

We introduce completely monotonic functions of order
$r>0$ and show that the remainders in asymptotic expansions of the logarithm
of Barnes double gamma function and Euler's gamma function give rise to
completely monotonic functions of any positive integer order.

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