Study on the Application of Borel's Improved Lagrange Interpolation Formula

Abstract

Because Lagrange interpolation formula can not converge uniformly to any continuous function, how to improve its convergence has become an important content in the study of Lagrange interpolation formula. Borel has pointed out that the polynomial obtained by Lagrange interpolation formula can't approximate the interpolated function well in some cases. How to improve Lagrange interpolation formula to better approximate the interpolated function is an important problem for mathematicians at that time, and Borel is one of them. In this paper, the application research of the improved Lagrangian interpolation formula by Bohr is deeply discussed by using the relevant original documents.