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In the paper [3],we have shown that the function ∍ ⟼ HD ( ) ∊ R is real-analytic, where is the set of all parameters .In this paper, using a holomorphic function ∶ (C ⧵ {0}) × (C ⧵ {0}) ⟶ C ⧵ {0}, ( , ) = and the conjugacy property, we show that the Hausdorff dimension function ∍ ( , ) ⟼ HD , ∊ R is real analytic, where = ( ). Thisfunctionascribestothepolynomial , theHausdorffdimension of its Julia set ( , ).

Real Analyticity of Hausdorff Dimension Function of Disconnected Julia Sets of Parabolic Polynomials fa,b(z) = z(1 – az – bz<sup>2</sup>)