Some properties of extended remainder of Binet's first formula for logarithm of gamma function

Abstract

In the paper, we extend Binet's first formula for the logarithm of the gamma function and investigate some properties, including inequalities, star-shaped and sub-additive properties and the complete monotonicity, of the extended remainder of Binet's first formula for the logarithm of the gamma function and related functions.

arXiv comment8 pages

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