  We prove that for any given upper semicontinuous function $\varphi$ 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 $\varphi$ on $E$, can be represented
as an envelope of a disc functional.
