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An inequality for generalized complete elliptic integral.

Li Yin1, Li-Guo Huang1, Yong-Li Wang2

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

Journal of Inequalities and Applications
|December 16, 2017
PubMed
Summary
This summary is machine-generated.

This study presents a novel inequality for generalized complete elliptic integrals of the first kind. It extends a significant mathematical result by Alzer.

Keywords:
generalized complete elliptic integralshypergeometric functioninequalitypsi function

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Area of Science:

  • Mathematical Analysis
  • Special Functions

Background:

  • Generalized complete elliptic integrals of the first kind are fundamental in mathematical physics and advanced calculus.
  • Previous research, including work by Alzer, has explored inequalities related to these integrals.

Purpose of the Study:

  • To establish a new elegant inequality concerning the ratio of generalized complete elliptic integrals of the first kind.
  • To generalize a specific interesting result previously demonstrated by Alzer.

Main Methods:

  • The study employs analytical techniques to derive the proposed inequality.
  • Methods involve the manipulation and comparison of generalized complete elliptic integrals.

Main Results:

  • An elegant inequality involving the ratio of generalized complete elliptic integrals of the first kind is proven.
  • A known result by Alzer is successfully generalized.

Conclusions:

  • The findings contribute to the theory of special functions and inequalities.
  • This work offers a broader perspective on elliptic integral properties and their applications.