Bounds for the logarithm of the Euler gamma function and its derivatives

  title={Bounds for the logarithm of the Euler gamma function and its derivatives},
  author={H. Diamond and A. Straub},
  journal={arXiv: Classical Analysis and ODEs},
We consider differences between $\log \Gamma(x)$ and truncations of certain classical asymptotic expansions in inverse powers of $x-\lambda$ whose coefficients are expressed in terms of Bernoulli polynomials $B_n(\lambda)$, and we obtain conditions under which these differences are strictly completely monotonic. In the symmetric cases $\lambda=0$ and $\lambda=1/2$, we recover results of Sonin, N\"orlund and Alzer. Also we show how to derive these asymptotic expansions using the functional… Expand
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