Functional inequalities for the incomplete gamma function

Horst Alzer, Árpád Baricz

Research output: Contribution to journalArticle

9 Citations (Scopus)


We present several inequalities for fa=Γ(a,x)/Γ(a,0) (a>0, x≥0) where Γ(a,x) is the incomplete gamma function. One of our theorems states that the inequalities. fa (Sp(x1,...,xn)) ≤ fa(x1)...fa(xn) ≤ fa(Sq(x1,...,xn)) (p,q>0) hold for all nonnegative real numbers x1,...,xn (n≥2) if and only if p≤min(a,1) and q≥max(a,1). Here, St(x1,...,xn) denotes the power sum of order t. This extends and complements a result published by Ismail and Laforgia in 2006.

Original languageEnglish
Pages (from-to)167-178
Number of pages12
JournalJournal of Mathematical Analysis and Applications
Issue number1
Publication statusPublished - Jan 1 2012


  • Arithmetic, geometric, and harmonic means
  • Completely monotonic
  • Concave
  • Convex
  • Functional inequalities
  • Grünbaum-type inequality
  • Incomplete gamma function
  • Power means
  • Power sums
  • Subadditive
  • Turán-type inequality

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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