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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

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On some inequalities for the incomplete gamma function
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by Horst Alzer PDF
Math. Comp. 66 (1997), 771-778 Request permission


Let $p\ne 1$ be a positive real number. We determine all real numbers $\alpha = \alpha (p)$ and $\beta =\beta (p)$ such that the inequalities \[ [1-e^{-\beta x^p}]^{1/p}< \frac 1{\Gamma (1+1/p)} \int ^x_0 e^{-t^p} dt <[1-e^{-\alpha x^p}]^{1/p}\] are valid for all $x>0$. And, we determine all real numbers $a$ and $b$ such that \[ -\log (1-e^{-ax})\le \int ^\infty _x \frac {e^{-t}}t dt\le -\log (1-e^{-bx})\] hold for all $x>0$.
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Additional Information
  • Horst Alzer
  • Affiliation: Morsbacher Str. 10, 51545 Waldbröl, Germany
  • MR Author ID: 238846
  • Received by editor(s): May 10, 1995
  • Received by editor(s) in revised form: April 5, 1996
  • © Copyright 1997 American Mathematical Society
  • Journal: Math. Comp. 66 (1997), 771-778
  • MSC (1991): Primary 33B20; Secondary 26D07, 26D15
  • DOI:
  • MathSciNet review: 1397438