Minimizing the error function of Gauss–Jacobi quadrature rule with respect to parameters α and β

In this paper we discuss about the error function of Gauss–Jacobi quadrature rule, equation(1)Zn(α,β)=f(2n)(ξ)(2n)!·2α+β+2n+1n!Γ(α+n+1)Γ(β+n+1)Γ(α+β+n+1)(α+β+2n+1)Γ(α+β+2n+1)2,α,β⩾-1;-1⩽ξ⩽1and then we optimize this function, and find the corresponding values of α and β, finally introduce some examples to illustrate the results.