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Absolute monotonicity of the accuracy of Ramanujan approximations for perimeter of an ellipse

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Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Aims and scope Submit manuscript

Abstract

In this paper, we prove that the absolute errors of 11 mean value approximations for the perimeter of an ellipse are all absolutely monotonic with respect to the eccentricity of this ellipse. More interestingly, we find that the relative errors of two Ramanujan approximations have the same property.

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Authors and Affiliations

  1. Department of Mathematics and Physics, North China Electric Power University, Yonghua Street 619, Baoding, 071003, People’s Republic of China

    Jing-Feng Tian

  2. Hebei Key Laboratory of Physics and Energy Technology, North China Electric Power University, Yonghua Street 619, Baoding, 071003, People’s Republic of China

    Jing-Feng Tian

  3. Department of Science and Technology, State Grid Zhejiang Electric Power Company Research Institute, Hangzhou, 310014, Zhejiang, People’s Republic of China

    Zhen-Hang Yang

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  1. Jing-Feng Tian
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  2. Zhen-Hang Yang
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Tian, JF., Yang, ZH. Absolute monotonicity of the accuracy of Ramanujan approximations for perimeter of an ellipse. Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat. 117, 135 (2023). https://doi.org/10.1007/s13398-023-01465-z

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