Z. SebestyénGödöllö University of Agricultural Sciences Department of Mathematics Faculty of Agricultural Engineering Páter K. U. 1 2103 Gödöllö Hungary
З. ЩебещтяенGödöllö University of Agricultural Sciences Department of Mathematics Faculty of Agricultural Engineering Páter K. U. 1 2103 Gödöllö Hungary
be the generalizednth Laguerre polynomial,n=1,2,… Letx1,x2,…,xn andx*1,x*2,…,x*n−1 denote the roots ofLn(α)
(x) andLn(α)′
(x) respectively and putx*0=0. In this paper we prove the following theorem:
Ify0,y1,…,yn−1 andy1′
,…,yn′
are two systems of arbitrary real numbers, then there exists a unique polynomialP(x) of degree 2n−1 satisfying the conditions