Some bounds for the elliptical integral of the first kind-Reference-Cited by-同舟云学术

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Some bounds for the elliptical integral of the first kind

Published:2023-06-01 Issue:1 Volume:31 Page:59-65
ISSN:1584-3289
Container-title:General Mathematics
language:en
Short-container-title:

Author:

Birou Marius-Mihai¹

Affiliation:

1. 1 Technical University of Cluj Napoca, România, Faculty of Automatics and Computer Science , Department of Mathematics , 28 Memorandumului Str., Cluj Napoca , România

Abstract

Abstract In this article we present a method to get upper bound for some integrals. The method is in connection with on a generalized trapezoidal quadrature formula. Applications for upper bounds of the elliptical integral of the first kind are presented. We compare these bounds with some previous results from the literature.

Publisher

Walter de Gruyter GmbH

Subject

General Medicine

Link

https://www.sciendo.com/pdf/10.2478/gm-2023-0006

Reference9 articles.

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.

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