The Vector QD Algorithm for Smooth Functions (f, f′) Original Research Article

We deal with the functionz↦(f(z), f′(z)) wheref(z)=∑i⩾0 aizi, (ai∈C) with limi→∞ ai+1×ai−1/(ai)2=q. We investigate the convergence of the vector QD algorithm. We give the asymptotic behaviour of the generalized Hankel determinants. A convergence result on the vector orthogonal polynomials is proved.