# 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} }

We prove that for all x > 0, we have with the best possible constants α = 0 and $\beta=\tfrac{1}{1620}$.

## 28 Citations

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A new continued fraction approximation and some inequalities for the gamma function are established and some numerical computations are given for demonstrating the superiority of the new series over the classical ones.

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