A \((0,2)\)-type Pál interpolation problem

Abstract. We consider the following Pál interpolation problem: On two sets of nodes (one consists of the zeros of a polynomial \(p_n\) of degree \(n\), while the elements of the other one are the zeros of \(p'_n\)) different interpolation conditions are prescribed simultaneously. Weighted \((0,1,\dots,r-2,r)\)-interpolation conditions \((r\geq 2)\) are given on one of the sets of the nodes with Hermite conditions on the other set. We study the regularity of the problem and the explicit representation of the fundamental polynomials of interpolation. We obtain regular examples on the zeros of the classical orthogonal polynomials.