Summary: Let the iterated function system (IFS) \(\{S_j\}^{m-1}_{j=0}\) be of the form \(S_j (z)=\varepsilon_j+\rho_j (z-\varepsilon_j)\), \(0<\rho_j<1\), \(|\varepsilon_j|\leq 1\), with at least one \(|\varepsilon_j|=1\), let \(K\) be the attractor of \(\{S_j\}^{m-1}_{j=0}\) and \(\mu\) be the Hausdorff measure supported on \(K\). Recently, X.-H. Dong and K.-S. Lau [J. Funct. Anal. 202, No. 1, 67–97 (2003; Zbl 1032.28005)] have studied the Laurent coefficient of a transform \(F (z)=\int_K (z-w)^{-1}d\mu (w)\) of a Hausdorff measure in \(|z|>1\). In this paper, we mainly consider the Laurent coefficients of \(G (z)=\int_K (\lambda z-w)^{-1}d\mu (w)\) in \(|z|>\dfrac1{|\lambda|} (|\lambda|\geq 1)\), and get some results.