AbstractWe define a class of formal expansions ∑ α𝓁z𝓁 of a rational function with at least one non‐zero pole. To distinct formal expansions ∑ α𝓁z𝓁 and ∑ β𝓁z𝓁 in this class we associate structured arrays A=(aij) and B =(bij), defined by aij=∑avα and bij=∑avβ, where q(≠0), p1,…,pk, and τ1,…,τk are integers and a1,…,ak are non‐zero complex constants. We study the asymptotic relationship between the singular values of the matrices (aij) and (bij) as min(hn, kn)→∞. Copyright © 2004 John Wiley & Sons, Ltd.