Simultaneous Approximation To A Interpolatory Polynomials And Its Derivative On The Roots Of Laguerre Polynomials By Pál-Type Interpolation

Abstract

The objective of this paper is to construct a interpolatory polynomial with Laguerre conditions based on the zeros of the polynomials  and  where  is the Laguerre polynomial of degree n and the derivative of Laguerre polynomial is of degree. A modified Pál-type interpolation problem is studied in a unified way. We prove the regularity of the problem and give the explicit formulae of the interpolation. Also, the existence and uniqueness of the polynomial is proved if the inner nodal points are the roots of the interpolatory polynomials and obtain an estimate over the whole real number line.

Mathematics Subject Classification 2000; 41A10, 97N50.