Approximation for the complete elliptic integral of the first kind

In the article, we present several sharp upper and lower bounds for the complete elliptic integral of the first kind in terms of inverse trigonometric and inverse hyperbolic functions. As consequences, some sharp bounds for the Gaussian arithmetic-geometric mean in terms of other bivariate means are...

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Bibliographic Details
Published inRevista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas Vol. 114; no. 2
Main Authors Qian, Wei-Mao, He, Zai-Yin, Chu, Yu-Ming
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.04.2020
Springer Nature B.V
Subjects
Applications of Mathematics
Bivariate analysis
Hyperbolic functions
Integrals
Lower bounds
Mathematical analysis
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Original Paper
Theoretical
26E60
Complete elliptic integrals
Arithmetic-geometric mean
33E05
Inverse trigonometric function
Inverse hyperbolic function
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Summary:In the article, we present several sharp upper and lower bounds for the complete elliptic integral of the first kind in terms of inverse trigonometric and inverse hyperbolic functions. As consequences, some sharp bounds for the Gaussian arithmetic-geometric mean in terms of other bivariate means are also given.
ISSN:1578-7303
1579-1505
DOI:10.1007/s13398-020-00784-9