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

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/220184We 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.13 pages, to appear in Journal of Mathematical Analysis and ApplicationsClassical Analysis and ODEsFunctional Analysis33B15; 41A60Completely monotonic functions of positive order and asymptotic expansions of the logarithm of Barnes double gamma function and Euler's gamma functiontext