A generalization of Pál interpolation process. II (Q1297750)

[For part I see \textit{I. Joó} and \textit{V. E. S. Szabó}, Acta Sci. Math. 60, No. 3-4, 429-438 (1995; Zbl 0830.41004).] Let \(-\infty<x_1<\ldots<x_k<x_{k+1}<\ldots<x_n<\infty\) be distinct nodes and \(\omega(x)=\prod^n_{k=1}(x-x_k)\) and \(\omega'(x)=n\prod^{n-1}_{k=1}(x-x'_k)\). For \(b,a',b'\in\mathbb{R}\) let \(x^*_k\) \((k=1,\dots,n^*)\) be the roots of the polynomial \(\Omega(x):=b\cdot\omega(x)+(a'x+b')\cdot\omega'(x)\). The author determines a unique polynomial \(R(x)\) of maximal degree which verifies the conditions (1) \(R(x_k)=y_k\), \(k=1,2,\dots,n\); \(R'(x_k^*)=y'_k\), \(k=1,2,\dots,n^*\) and obtains an explicit formula of the polynomial \(R(x)\) of degree \(n+n^*-1\) in the case when \(b<0\), \(a'=1\), \(b'\neq-1\) and \(\Omega(x)\) has real distinct roots.