An Interpolation Process on Laguerre Abscissas with an Additional condition

Abstract

This paper is devoted to studying a P ́al-type interpolation problem on the roots of Laguerre polynomials of degree n and its derivative of degree n − 1. In this paper, we study an interpolation on the polynomials with an additional condi- tion on the zeros of Laguerre polynomials. The mixed type (0,1;0)-interpolation problem is studied in a unified way. The objective of this study is to identify a single interpolatory polynomial with degree at most 3n + k that satisfies the interpolatory requirements. In the regular cases we find the explicit forms of the interpolational polynomials. Under certain conditions over the Laguerre polynomial and its derivative, we also obtain the estimates of the fundamental polynomials on the whole real line.