On rational Lagrange interpolation with poles at the boundary

K. Manral, S. Bahadur

This article considers Lagrange interpolation with poles -1 and 1 interpolating a function f on the zeros X of the Jacobi polynomial, Pn(α,β)(x); α, β > -1. The corresponding Lebesgue constant is estimated. The uniform convergence of the Lagrange interpolation is obtained on D=[a,b]⊂(-1,1) such that X⊆D. At last, some numerical experiments are presented. 

Advanced Studies: Euro-Tbilisi Mathematical Journal, Vol. 18(1) (2025), pp. 163-171