Monotonicity properties and bounds involving the complete elliptic integrals of the first kind
By Zhen-Hang Yang, Wei-Mao Qian, Y. Chu. 2018
75 citations recorded by the source corpus.
In the article, we establish several monotonicity properties of the functions involving the complete elliptic integral of the first kind. As applications, we present sharp bounds for the complete elliptic integral of the first kind and the arithmetic-geometric mean. Mathematics subject classification (2010): 33E05, 26E60.
Subfields: Applied Mathematics, Computational Theory and Mathematics
View Paper: https://www.semanticscholar.org/paper/cf60cfb13bd8dcd0ac6f2aee578eeaa2e0311bee
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In Applied Mathematics
In Computational Theory and Mathematics
Citations in the corpus
- Sharp bounds for the Toader mean of order 3 in terms of arithmetic, quadratic and contraharmonic means (2020, background): “The complete elliptic integral K(r) (0 < r < 1) [1,7,8,11,23,27,32,39,40,43,46,48,51] of the first kind is closely related to the complete elliptic integral E(r) of the second kind, which is defined by”