We give an elementary proof of the product formula for the multivariate transfinite diameter using multivariate Leja sequences and an identity on vandermondians.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ba53-3-7, author = {Jean-Paul Calvi and Phung Van Manh}, title = {A Determinantal Proof of the Product Formula for the Multivariate Transfinite Diameter}, journal = {Bulletin of the Polish Academy of Sciences. Mathematics}, volume = {53}, year = {2005}, pages = {291-298}, zbl = {1109.32028}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba53-3-7} }
Jean-Paul Calvi; Phung Van Manh. A Determinantal Proof of the Product Formula for the Multivariate Transfinite Diameter. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 53 (2005) pp. 291-298. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba53-3-7/