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Certain inequalities involving the k-Struve function.

Kottakkaran Sooppy Nisar1, Saiful Rahman Mondal2, Junesang Choi3

  • 1Department of Mathematics, College of Arts and Science-Wadi Aldawaser, Prince Sattam bin Abdulaziz University, Wadi Ad-Dawasir, Riyadh region 11991 Saudi Arabia.

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|April 28, 2017
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Summary

This study introduces the k-Struve function, exploring its properties and inequalities, including a novel Turán-type inequality. The research also details its differential equation, recurrence relations, and integral representations.

Keywords:
Turán-type inequalitiesk-Struve functionk-beta functionk-digamma functionk-gamma function

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Area of Science:

  • Mathematical Analysis
  • Special Functions

Background:

  • Special functions are crucial in various scientific fields.
  • The Struve function is a well-known special function with existing properties.
  • Further exploration of generalized Struve functions can yield new mathematical insights.

Purpose of the Study:

  • Introduce and define the k-Struve function.
  • Investigate the mathematical properties of the k-Struve function.
  • Establish inequalities and relationships for the k-Struve function.

Main Methods:

  • Definition of the k-Struve function.
  • Derivation of inequalities, including a Turán-type inequality.
  • Development of a differential equation and recurrence relations.
  • Formulation of integral representations.

Main Results:

  • The k-Struve function is formally defined.
  • Several inequalities associated with the k-Struve function are proven.
  • A connection to the classical Turán-type inequality is established.
  • A differential equation, recurrence relations, and integral representations are presented.

Conclusions:

  • The k-Struve function is a novel mathematical entity with diverse properties.
  • The established inequalities and relations provide a foundation for further research.
  • This work expands the family of generalized Struve functions.