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On a function involving generalized complete (pq)-elliptic integrals

  • Barkat Ali BhayoEmail author
  • Li Yin
Open Access
Article
  • 12 Downloads

Abstract

Motivated by the work of Alzer and Richards (Anal Math 41:133–139, 2015), here authors study the monotonicity and convexity properties of the function
$$\begin{aligned} \Delta _{p,q} (r) = \frac{{E_{p,q}(r) - \left( {r'} \right) ^p K_{p,q}(r) }}{{r^p }} - \frac{{E'_{p,q}(r) - r^p K'_{p,q}(r) }}{{\left( {r'} \right) ^p }}, \end{aligned}$$
where \(K_{p,q}\) and \(E_{p,q}\) denote the complete (pq)-elliptic integrals of the first and second kind, respectively.

Mathematics Subject Classification

33C99 33B99 

Notes

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© The Author(s) 2019

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Department of mathematicsSukkur IBA UniversitySindhPakistan
  2. 2.Faculty of Engineering and natural sciencesSabanci UniversityTuzlaTurkey
  3. 3.Department of MathematicsBinzhou UniversityBinzhouChina

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