A convergence theorem for the Pál method of interpolation on the roots of Hermite polynomials

An evaluation of weighted polynomial interpolation with certain conditions on the roots of Hermite polynomial

“…In 1985, L. Szili [15] applied this interpolation process by taking the mixed zeroes of H n (x) and its derivative on infinite interval. For n even, he showed that there exists a uniquely determined polynomial P * n (x) of degree ≤ 2n−1, satisfying the conditions:…”

(0,1;0)-Interpolation on infinite interval (−∞, +∞)

“…Szili [11] was the first to apply this method on infinite interval by taking the mixed zeros of H n (x) and its derivative H n (x). For n even, he showed that there exists a uniquely determined polynomial of degree ≤ 2n-1 satisfying the conditions:…”

“…Recently, Z.F.Sebéstyen [8] has modified the results of L.Szili [11] and I.Joó [5] by replacing the condition (1.3) by an interpolatory condition R n (0) = α 0 for n even and also showed that for n odd there exists a unique polynomial of degree ≤2n-1 satisfying the conditions (1.2) and R n (0) = α 0 .…”

On (0;1) Pál-type interpolation with boundary conditions

“…For the uniqueness Eneduanya used also the additional nodal point x * n = −1. Szili [15] investigated the Pál-type interpolation on the roots of the Hermite-polynomials with the additional point x 0 = 0. Both Eneduanya and Szili gave explicit formulae and proved approximation theorems.…”