Complete Hyper-elliptic Integrals of the First
Kind and the Chebyshev Property |
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Authors: | Jihua Yang |
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Institution: | School of Mathematics and Computer Science, Ningxia Normal University, Guyuan, Ningxia 756000, China |
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Abstract: | This paper is devoted to study 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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Keywords: | Complete hyper-elliptic integral of the first kind Chebyshev
ECT-system |
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