Weighted Pál type (1;0)-interpolation on the zeros of Laguerre abscissas

Abstract

In this paper, we have studied a Pál type (1; 0)-interpolation when first derivatives and function values are prescribed on the zeros of Laguerre Polynomials $L_{n}^{(\alpha)}(x), \alpha > -1$ and its derivative $(L_{n}^{(\alpha)})^{\prime}(x)$ respectively. Existence, uniqueness, explicit representation and a quantitative estimate of the interpolatory polynomial $R_{n, \alpha}(x)$ has been obtained.