Lagrange and Hermite interpolation processes on the positive real line (Q1107751)

We consider interpolation based on the Laguerre roots and the point 0 as nodes. First we show that this interpolation generates a convergent approximation process on [0,\(\infty)\) for a wide class of functions. Moreover, we prove the following interesting fact: In order to have uniform convergence of the derivatives of the interpolating polynomials in every interval [0,A], it is sufficient to prescribe the derivatives at 0 only, in addition to the function values at the above-mentioned nodes.