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In this paper we consider the meromorphic function $G(z)$ with a pole of order $1$ at $-a$ and analytic function $F(z)$ with a zero $-a$ of order 2 in ${\Bbb D}= \{ z : |z| < 1 \}$, where $-1<a<1.$  From these functions we obtain the regular simply-connected minimal surface $S=\{(u(z),v(z), H(z)) : z \in {\Bbb D} \}$ in $E^3$ and the harmonic function $ f = u + iv $ defined on $\Bbb D$, and then we investigate properties of the minimal surface $S$ and the harmonic function $f$.

HARMONIC MAPPING RELATED WITH THE MINIMAL SURFACE GENERATED BY ANALYTIC FUNCTIONS