A New Kind of Weighted (0;0,2) Interpolation on Laguerre Polynomial

In this paper we consider a special problem of mixed type (0, 0, 2) interpolationon on the two sets of the nodes of Laguerre polynomial in which one set consists of the nodes of L_n^k (x) while the other are nodes of L_n^ (k-1) (x). We prove the existence, uniqueness and explicit representation of fundamental polynomials on infinite interval.