(0, 2) – Interpolation of Entire Functions
Robert Gervais, Qazi Ibadur Rahman, Gerhard Schmeißer · Canadian Journal of Mathematics · 1986
Given a triangular matrix A whose nth row consists of the n points (1.1) Turán et al. ([12], [1], [2], [3]) considered the problem of existence, uniqueness, representation, convergence, etc. of polynomials f2n – 1 of degree ≧2n – 1 where the values of f2n – 1 and those of its second derivative are prescribed at the points (1.1), i.e., (1.2) The choice of the points (1.1) is important. They found the zeros (1.3) of the polynomial (1.1) where Pn – 1 is the (n − 1) Legendre polynomial with the normalization Pn – 1(l) = 1 to be the most convenient.