Simultaneous Inverse Approximation To A Laguerre Polynomials and its Derivative by Pál-Type Interpolation

Abstract

Using the zeros of the polynomials, the aim of this work is to create an interpolatory polynomial with Laguerre conditions, where  is the Laguerre polynomial of degree n and whose derivative  is of degree . A unified study of a modified inverse Pál-type interpolation issue is conducted. We have proved the explicit interpolation equations and demonstrate the problem's regularity. Additionally, if the inner nodal points are the roots of the interpolatory polynomials and yield an estimate over the whole real number line, the polynomial's existence and uniqueness are demonstrated.