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On Generalized Complete (p, q)-Elliptic Integrals

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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 Turán type inequalities are given. Finally, we also show some new series representations of these functions by applying Alzer and Richard’s methods.

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Authors and Affiliations

  1. College of Science, Binzhou University, Binzhou City, 256603, China

    Li Yin

  2. Department of Mathematics, Sukkur IBA University, Sukkur, Sindh, Pakistan

    Barkat Ali Bhayo

  3. Faculty of Natural Sciences, Sabanci University, 34956, Tuzla/Istanbul, Turkey

    Nihat Gökhan Göğüş

Authors
  1. Li Yin
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  2. Barkat Ali Bhayo
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  3. Nihat Gökhan Göğüş
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Correspondence to Li Yin.

Additional information

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).

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Yin, L., Bhayo, B.A. & Göğüş, N.G. On Generalized Complete (p, q)-Elliptic Integrals. Acta Math Sci 41, 475–486 (2021). https://doi.org/10.1007/s10473-021-0211-4

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  • DOI: https://doi.org/10.1007/s10473-021-0211-4

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