The completeness of a functional sequence

Let $\{\pi_n(u)\}$ be a sequence of polynomials with a biorthogonal system, and let $\{\mathscr{P}_n(z)\}$ be functions defined in the singly connected domain $\mathrm{D}$. We consider the problem of the completeness of the system
$$ A(z,\lambda_n)=\sum_{s=0}^\infty\mathscr{P}_s(z)\pi_s(\lambda_n),\qquad n=1,2,\dots, $$
in the class of functions $\mathrm{F(z)}$ having the representation
$$ F(z)=\sum_{k=0}^\infty d_k \mathscr{P}_k(z). $$