2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/219226Weighted pluripotential theory is a rapidly developing area; and Callaghan \cite{Callaghan} recently introduced $θ$-incomplete polynomials in \cd for $d>1$. In this paper we combine these two theories by defining weighted $θ$-incomplete pluripotential theory. We define weighted $θ$-incomplete extremal functions and obtain a Siciak-Zahariuta type equality in terms of $θ$-incomplete polynomials. Finally we prove that the extremal functions can be recovered using orthonormal polynomials and we demonstrate a result on strong asymptotics of Bergman functions in the spirit of \cite{BermanCn}.27 Pages, A new theorem added, Some corrections madeComplex Variables32U20, 32U15text