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Turán type inequalities for generalized Mittag-Leffler function.

Xiang Kai Dou1, Li Yin1

  • 1Department of Mathematics, Binzhou University, Binzhou City, Shandong Province 256603 China.

Journal of Inequalities and Applications
|September 22, 2017
PubMed
Summary
This summary is machine-generated.

This study establishes Turán type inequalities for a generalized Mittag-Leffler function using the [Formula: see text]-gamma function, advancing mathematical analysis.

Keywords:
Turán type inequalities[Formula: see text]-gamma functiongeneralized Mittag-Leffler function

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Area of Science:

  • Mathematical Analysis
  • Special Functions

Background:

  • Mittag-Leffler functions are crucial in various scientific fields.
  • Generalized versions extend their applicability.
  • Turán type inequalities provide bounds on function behavior.

Purpose of the Study:

  • To derive novel Turán type inequalities.
  • To focus on a generalized Mittag-Leffler function with four parameters.
  • To utilize the [Formula: see text]-gamma function in this derivation.

Main Methods:

  • Application of the [Formula: see text]-gamma function.
  • Development of analytical techniques for inequality derivation.
  • Focus on properties of the four-parameter generalized Mittag-Leffler function.

Main Results:

  • Several new Turán type inequalities were proven.
  • The inequalities are specific to the generalized Mittag-Leffler function.
  • The [Formula: see text]-gamma function proved instrumental.

Conclusions:

  • The findings expand the understanding of generalized Mittag-Leffler functions.
  • The derived inequalities offer valuable analytical tools.
  • This work contributes to the theory of special functions.