Completely monotonic functions of positive order and asymptotic expansions of the logarithm of Barnes double gamma function and Euler’s gamma function
نویسندگان
چکیده
In this paper it is established that the remainders in asymptotic expansions of the logarithm of Barnes double gamma function and Euler’s gamma function are (up to a sign) completely monotonic functions of order comparable with the decay of the remainder in the expansion. We first recall some definitions and give some preliminary results. A function f : (0, ∞) → R is called completely monotonic if f has derivatives of all orders and satisfies
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