Articles

ON GENERALIZED COMPLETE (p,q)-ELLIPTIC INTEGRALS

  • Li YIN ,
  • Barkat Ali BHAYO ,
  • Nihat Gökhan GÖĞüŞ
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  • 1. College of Science, Binzhou University, Binzhou City 256603, China;
    2. Department of Mathematics, Sukkur IBA University, Sindh, Pakistan;
    3. Faculty of Natural Sciences Sabanci University, 34956 Tuzla/Istanbul, Turkey
Barkat Ali BHAYO,E-mail:barkat.bhayo@iba-suk.edu.pk;Nihat Gökhan GÖĞÜŞ,E-mail:nggogus@sabanciuniv.edu

Received date: 2020-01-17

  Revised date: 2020-09-30

  Online published: 2021-04-29

Supported by

The first author was supported by the Natural Science Foundation of Shandong Province (ZR2019QA003 and ZR2018MF023), by the National Natural Science Foundation of China (11601036), and by the Major Project of Binzhou University (2020ZD02).

Abstract

In this paper, we study the generalized complete (p,q)-elliptic integrals of the first and second kind as an application of generalized trigonometric functions with two parameters, and establish the monotonicity, generalized convexity and concavity of these functions. In particular, some Tur\'an type inequalities are given. Finally, we also show some new series representations of these functions by applying Alzer and Richard's methods.

Cite this article

Li YIN , Barkat Ali BHAYO , Nihat Gökhan GÖĞüŞ . ON GENERALIZED COMPLETE (p,q)-ELLIPTIC INTEGRALS[J]. Acta mathematica scientia, Series B, 2021 , 41(2) : 475 -486 . DOI: 10.1007/s10473-021-0211-4

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