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High accuracy asymptotic bounds for the complete elliptic integral of the second kind

Author

Listed:
  • Yang, Zhen-Hang
  • Chu, Yu-Ming
  • Zhang, Wen

Abstract

In the article, we prove that the double inequalityπ2J(r′)−51π−160160r16

Suggested Citation

  • Yang, Zhen-Hang & Chu, Yu-Ming & Zhang, Wen, 2019. "High accuracy asymptotic bounds for the complete elliptic integral of the second kind," Applied Mathematics and Computation, Elsevier, vol. 348(C), pages 552-564.
    • Handle: RePEc:eee:apmaco:v:348:y:2019:i:c:p:552-564
    DOI: 10.1016/j.amc.2018.12.025
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    References listed on IDEAS

    as
    1. Yu-Ming Chu & Miao-Kun Wang, 2012. "Inequalities between Arithmetic-Geometric, Gini, and Toader Means," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-11, December.
    2. Tie-Hong Zhao & Yu-Ming Chu & Hua Wang, 2011. "Logarithmically Complete Monotonicity Properties Relating to the Gamma Function," Abstract and Applied Analysis, Hindawi, vol. 2011, pages 1-13, July.
    3. Yang, Zhen-Hang & Chu, Yu-Ming, 2015. "Asymptotic formulas for gamma function with applications," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 665-680.
    4. Zhen-Hang Yang & Yu-Ming Chu & Xiao-Jing Tao, 2014. "A Double Inequality for the Trigamma Function and Its Applications," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-9, July.
    5. Wang, Miao-Kun & Chu, Yu-Ming & Song, Ying-Qing, 2016. "Asymptotical formulas for Gaussian and generalized hypergeometric functions," Applied Mathematics and Computation, Elsevier, vol. 276(C), pages 44-60.
    6. Yu-Ming Chu & Miao-Kun Wang & Song-Liang Qiu & Ye-Fang Qiu, 2011. "Sharp Generalized Seiffert Mean Bounds for Toader Mean," Abstract and Applied Analysis, Hindawi, vol. 2011, pages 1-8, October.
    Full references (including those not matched with items on IDEAS)

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    Cited by:

    1. Zhen-Hang Yang & Jing-Feng Tian & Ya-Ru Zhu, 2020. "A Rational Approximation for the Complete Elliptic Integral of the First Kind," Mathematics, MDPI, vol. 8(4), pages 1-9, April.
    2. Chen, Wenbin & Gao, Fang & She, Jinhua & Xia, Weifeng, 2020. "Further results on delay-dependent stability for neutral singular systems via state decomposition method," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).

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