Complete Hyper-Elliptic Integrals of the First Kind and the Chebyshev Property

Complete Hyper-Elliptic Integrals of the First Kind and the Chebyshev Property

Year:    2020

Author:    Jihua Yang

Journal of Nonlinear Modeling and Analysis, Vol. 2 (2020), Iss. 3 : pp. 431–446

Abstract

This paper is devoted to studying the following complete hyper-elliptic integral of the first kind $$J(h)=\oint\limits_{\Gamma_h}\frac{\alpha_0+\alpha_1x+\alpha_2x^2+\alpha_3x^3}{y}dx,$$ where $\alpha_i\in\mathbb{R}$, $\Gamma_h$ is an oval contained in the level set $\{H(x,y)=h, h\in(-\frac{5}{36},0)\}$ and $H(x,y)=\frac{1}{2}y^2-\frac{1}{4}x^4+\frac{1}{9}x^9$. We show that the 3-dimensional real vector spaces of these integrals are Chebyshev for $\alpha_0=0$ and Chebyshev with accuracy one for $\alpha_i=0\ (i=1,2,3)$.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.12150/jnma.431

Journal of Nonlinear Modeling and Analysis, Vol. 2 (2020), Iss. 3 : pp. 431–446

Published online:    2020-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    16

Keywords:    Complete hyper-elliptic integral of the first kind Chebyshev ECT-system.

Author Details

Jihua Yang