Z. SebestyénGödöllő University of Agricultural Sciences Department of Mathematics Faculty of Agricultural Engineering Páter K. U. 1 2103 Gödöllő Hungary
Э. СебестяянGödöllő University of Agricultural Sciences Department of Mathematics Faculty of Agricultural Engineering Páter K. U. 1 2103 Gödöllő Hungary
Letx*1, …,x*n−1 be the roots of the derivativeω′n(x) and putx0=0.
In this paper, the following theorem is proved: Ify0, …,yn andy′1, …,y′n−1 are arbitrary real numbers, then there exists a unique polynomialP2n−1(x) of degree 2n−1 having the following interpolation properties:
.
This result gives the theoretical completion of the original Pál type interpolation process, since it ensures uniqueness without
assuming any additional condition.