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Let $\mathbb{D}$ denote the unit disk in the complex plane. We
consider a class of superbiharmonic weight functions $w:
\mathbb{D}\rightarrow \mathbb{R}$ whose growth are subject to the
condition $0\leq w(z)\leq C(1-|z|)$ for some constant $C$. We
first establish a Riesz-type representation formula for $w$, and
then use this formula to prove that the polynomials are dense in
the weighted Bergman space with weight $w$.
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