Approximation properties for linear combinations of moment type operators

Here we give a Voronovskaja formula of high order for linear combinations of moment type convolution operators (Tn,rf)(s)=∫0+∞∑j=1rαjMjn(t)f(st)dtt, where MnMn is the moment kernel. This kind of operator provides a better order of pointwise approximation and leads to asymptotic formulae of type limn→+∞nr[(Tn,rf)(s)−f(s)]=A(f,r) where r∈Nr∈N and A(f,r)A(f,r) is a differential operator containing the derivatives of ff up to order rr.