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}
}
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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