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.