Approximation Properties of the Vallée-Poussin Means of Partial Sums of a Special Series in Laguerre Polynomials

We consider the problem of the approximation of functions, continuous on the semiaxis $[0,\infty)$ and for which the derivatives $f^{(\nu)}(0)$, $\nu=0,\dots,r-1$ exist at the point $x=0$, by the Vallée-Poussin means of partial sums of a special series in Laguerre polynomials.