Weighted (0,2) interpolation on the extended Tchebycheff nodes of second kind (Q1320461)

This paper is concerned with the following (0,2) interpolation problem: for prescribed numbers \(f_k\) and \(f_k''\) find a polynomial \(Q_n\) of degree at most \(2n+1\) such that \(Q_n(x_k)=f_k\), \(0\leq k\leq n+1\), \[ \bigl[(1-x^2)^{3/4} Q_n(x)\bigr]_{x=x_k}'' =f_k'', \] where \(x_0=1\), \(x_{n+1}=-1\), \(x_k= \cos(k\pi/(n+1))\), \(1\leq k\leq n\). For this interpolation problem the author discusses the questions of existence, uniqueness, representation of fundamental polynomials and convergence (when the corresponding parameters represent function and derivative values).