(untitled) (Journal of Nonlinear Modeling and Analysis, 2024)
This paper is devoted to studying the following complete hyper-elliptic integral of the first kind J(h)=_Γ_hα_0+α_1x+α_2x^2+α_3x^3ydx, where α_iR, Γ_h is an oval contained in the level set {H(x,y)=h, h(-536,0)} and H(x,y)=12y^2-14x^4+19x^9. We show that the 3-dimensional real vector spaces of these integrals are Chebyshev for α_0=0 and Chebyshev with accuracy one for α_i=0 (i=1,2,3).