2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/144438We provide a general framework and indicate relations between the notions of transfinite diameter, homogeneous transfinite diameter, and weighted transfinite diameter for sets in C^N. An ingredient is a formula of Rumely which relates the Robin function and the transfinite diameter of a compact set. We also prove limiting formulas for integrals of generalized Vandermonde determinants with varying weights for a general class of compact sets and measures in C^N. Our results extend to certain weights and measures defined on cones in R^N.Complex VariablesClassical Analysis and ODEs32U20; 42C05text