A note on weighted homogeneous Siciak-Zaharyuta extremal functions

We prove that for any given upper semicontinuous function $\phi$ on an open subset $E$ of ${\mathbb{C}}^n\setminus \{0\}$, such that the complex cone generated by $E$ minus the origin is connected, the homogeneous Siciak-Zaharyuta function with the weight $\phi$ on $E$, can be represented as an envelope of a disc functional.