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# On some inequalities for the incomplete gamma function

@article{Alzer1997OnSI, title={On some inequalities for the incomplete gamma function}, author={Horst Alzer}, journal={Math. Comput.}, year={1997}, volume={66}, pages={771-778} }

- Published 1997 in Math. Comput.
DOI:10.1090/S0025-5718-97-00814-4

Let p 6= 1 be a positive real number. We determine all real numbers α = α(p) and β = β(p) such that the inequalities [1− e−βx p ] < 1 Γ(1 + 1/p) ∫ x 0 e−t p dt < [1− e−αx p ] are valid for all x > 0. And, we determine all real numbers a and b such that − log(1− e−ax) ≤ ∫ ∞ x e−t t dt ≤ − log(1− e−bx)

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