On the growth of polynomials
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Abstract
In this paper, we study the growth of polynomials $P(z)$ of degree $n$ defined by $P(z)=z^s(a_0+\sum\limits_{j=t}^{n-s}a_j z^j),\quad t\geq 1,\quad 0\leq s\leq n-1$ which do not vanish in the disk $|z|\leq k, \quad k\geq 1$ except for the $s$-fold zeros at origin. Our result generalises and refines many results known in the literature.
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