2008•arXiv (Cornell University)Open access

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

Stamatis Koumandos, H. Pedersen

Abstract

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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Key concepts: Monotonic function, Gamma function, Logarithm, Mathematics, Euler's formula, Integer (computer science), Function (biology), Order (exchange)