Integral representations and complete monotonicity related to the remainder of Burnside’s formula for the gamma function

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摘要

In the paper, the authors establish integral representations of some functions related to the remainder of Burnside’s formula for the gamma function and find the (logarithmically) complete monotonicity of these and related functions. These results extend and generalize some known conclusions.

论文关键词：primary,33B15,secondary,26A48,26A51,33B10,41A30,41A60,44A10,Integral representation,Complete monotonicity,Logarithmically completely monotonic function,Remainder,Burnside’s formula,Gamma function

论文评审过程：Received 23 January 2014, Revised 2 March 2014, Available online 17 March 2014.

论文官网地址：https://doi.org/10.1016/j.cam.2014.03.004