Z. SebestyénGödöllö University of Agricultural Sciences Department of Mathematics Faculty of Agricultural Engineering Páter K. U. 1 2103 Gödöllő Hungary
З. ЩебещтяенGödöllö University of Agricultural Sciences Department of Mathematics Faculty of Agricultural Engineering Páter K. U. 1 2103 Gödöllő Hungary
be thenth Legendre polynomial. Letx1,x2,…,xn andx*1,x*2,…,x*n−1 denote the roots ofPn(x) andP′n(x), respectively. Putx0=x*0=−1 andx*n=1. In this paper we prove the following theorem: Ify0,y1,…,yn andy′0,y′1, …,y′n are two systems of arbitrary real numbers, then there exists a unique polynomialQ2n+1(x) of degree at most 2n+1 satisfying the conditions