Sharp upper and lower bounds for the gamma function

@article{Alzer2009SharpUA,
  title={Sharp upper and lower bounds for the gamma function},
  author={Horst Alzer},
  journal={Proceedings of the Royal Society of Edinburgh: Section A Mathematics},
  year={2009},
  volume={139},
  pages={709 - 718}
}
  • H. Alzer
  • Published 8 July 2009
  • Mathematics
  • Proceedings of the Royal Society of Edinburgh: Section A Mathematics
We prove that for all x > 0, we have with the best possible constants α = 0 and $\beta=\tfrac{1}{1620}$. 

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