@Article{JNMA-2-431,
author = {Yang , Jihua},
title = {Complete Hyper-Elliptic Integrals of the First Kind and the Chebyshev Property},
journal = {Journal of Nonlinear Modeling and Analysis},
year = {2021},
volume = {2},
number = {3},
pages = {431--446},
abstract = {<p style="text-align: justify;">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 $\alpha_i=0\ (i=1,2,3)$.</p>},
issn = {2562-2862},
doi = {https://doi.org/10.12150/jnma.431},
url = {http://global-sci.org/intro/article_detail/jnma/18820.html}
}