An asymptotic expansion for the error in a linear map that reproduces polynomials of a certain order

holds, with E(f, x) explicitly given as an integral involving Df . Since, for his particular choice of L, the sum involves the derivatives of f at the points or nodes xi associated with L, Han thinks of this as a ‘multinode’ expansion for f . It is the purpose of this note to point out that this asymptotic error expansion, properly interpreted, holds for any bounded linear map L on C([a . . b]), with the same formula for E(f, x). The key is the formula for the divided difference at a sequence containing just two distinct points. It is easy to verify, for example by induction on r and m, particularly for the special case x = 0, y = 1, that, for any x 6= y,