On rational Hermite-Fejér interpolation

This article focuses on the study of Hermite-Fej? r interpolation in a rational space. We con-structed the rational functions with poles -1, 1 satisfying the conditions of the Hermite-Fej? r interpolation on the nodes of the orthogonal Jacobi polynomial. The objective is to determine the quantitative esti-mate of the corresponding interpolatory function. Further, some numerical simulations are performed to demonstrate the effectiveness of the theory of the research work.