On rational Lagrange interpolation with poles at the boundary

This article considers Lagrange interpolation with poles $-1$ and $1$ interpolating a function $f$ on the zeros $X$ of the Jacobi polynomial, $P_n^{(\alpha,\beta)}(x);\alpha,\beta>-1$. The corresponding Lebesgue constant is estimated. The uniform convergence of the Lagrange interpolation is obtained on $\overline{D}=[a,b]\subset(-1,1)$ such that $X\subseteq \overline{D}$. At last, some numerical experiments are presented.