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Some bounds for the elliptical integral of the first kind Cover

Some bounds for the elliptical integral of the first kind

Open Access
|Nov 2023

References

  1. H. Alzer, Sharp inequalities for the complete elliptic integral of the first kind, Math. Proc. Camb. Philos. Soc., 124, 1998, 309-314.
  2. H. Alzer, S. L. Qiu, Monotonicity theorems and inequalities for the complete elliptic integrals, J. Comput. Appl. Math., 172, 2004, 289-312.
  3. G. D. Anderson, M. K. Vamanamurthy, M. Vuorinen, Functional inequalities for hypergeometric functions and complete elliptic integrals, SIAM J. Math. Anal., vol. 23, no. 2, 1992, 512-524.
  4. D. Cardenas-Morales, P. Garrancho, I. Rasa, Bernstein type operators which preserve polynomials, Comp. Math. Appl., vol. 62, no. 1, 2011, 158-163.
  5. S. Karlin, W. Studden, Tchebycheff Systems: with Applications in Analysis and Statistics, Interscience, New York, 1966.
  6. S. L. Qiu, M. K. Vamanamurthy, Sharp estimates for complete elliptic integrals, SIAM J. Math. Anal., 27, 1996, 823-834.
  7. D. D. Stancu, G. Coman, P. Blaga, Numerical analysis and approximation theory, vol II, Presa Universitara Clujana, 2002 (Romanian).
  8. Z. H. Yang, W. M. Qian, Y. M. Chu, W. Zhang, On approximating the arithmetic-geometric mean and complete elliptic integral of the first kind, J. Math. Anal. Appl., 462, 2018, 1714-1726.
  9. Z. Ziegler, Linear approximation and generalized convexity, J. Approx. Theor., 1, 1968, 420-433.
DOI: https://doi.org/10.2478/gm-2023-0006 | Journal eISSN: 1584-3289 | Journal ISSN: 1221-5023
Language: English
Page range: 59 - 65
Submitted on: May 2, 2023
Accepted on: Jun 3, 2023
Published on: Nov 24, 2023
Published by: Lucian Blaga University of Sibiu
In partnership with: Paradigm Publishing Services
Publication frequency: 2 issues per year

© 2023 Marius-Mihai Birou, published by Lucian Blaga University of Sibiu
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.