On orthogonal Laurent polynomials related to the partial sums of power series

Let $f(z)={\sum }_{k=0}^{\mathrm{\infty }}{d}_k{z}^k$, $d_k\in \mathbb{C}\mathrm{\backslash }\{0\}$, $d_0=1$, be a power series with a non-zero radius of convergence $\rho$: $0<\rho \le +\mathrm{\infty }$. Denote by $f_n(z)$ the n-th partial sum of $f$, and $R_{2n}(z)=\frac{f_{2n}(z)}{z^n}$, $R_{2n+1}(z)=\frac{f_{2n+1}(z)}{z^{n+1}}$, $n=0,1,2,\mathrm{.}\mathrm{.}\mathrm{.}$. By the result of Hendriksen and Van Rossum there exists a linear functional $\mathbf{L}$ on Laurent polynomials, such that $\mathbf{L}(R_n{R}_m)=0$, when $n≠m$, while $\mathbf{L}(R_n^2)≠0$. We present an explicit integral representation for $\mathbf{L}$ in the above case of the partial sums. We use methods from the theory of generating functions. The case of finite systems of such Laurent polynomials is studied as well.