Log-concavity and log-convexity of series containing multiple Pochhammer symbols

Dmitrii Karp, Yi Zhang*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


In this paper, we study power series with coefficients equal to a product of a generic sequence and an explicitly given function of a positive parameter expressible in terms of the Pochhammer symbols. Four types of such series are treated. We show that logarithmic concavity (convexity) of the generic sequence leads to logarithmic concavity (convexity) of the sum of the series with respect to the argument of the explicitly given function. The logarithmic concavity (convexity) is derived from a stronger property, namely, positivity (negativity) of the power series coefficients of the so-called generalized Turánian. Applications to special functions such as the generalized hypergeometric function and the Fox-Wright function are also discussed.

Original languageEnglish
Pages (from-to)458-486
Number of pages29
JournalFractional Calculus and Applied Analysis
Issue number1
Publication statusPublished - Feb 2024


  • Fox-Wright function
  • Hypergeometric functions
  • Logarithmic concavity (primary)
  • Logarithmic convexity
  • Pochhammer symbol
  • Rising factorial
  • Turánian


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