Higher order Hermite-Fejer interpolation polynomials with Laguerre-type weights

摘要

Let R~+ = [0, oo) and R : R~+ → R~+ be a continuous function which is the Laguerre type exponent, and p_(n ,p)(x), p >-1/2 be the orthonormal polynomials with the weight w_p(x) = x~p e~(-r(x). For the zeros {x_(k,n,p)}_k=1~n of p_(n,P)(x) = p_n(w_p~2;x), we consider the higher order Hermite-Fejer interpolation polynomial L_n(l, m, f, x) based at the zeros {x_(k,n,p)}_k=1~n, where 0 ≤ l ≤ m - 1 are positive integers.