Holder theorem on Gamma fn, actual cite to proof
by Bank & Kauffman claims to be an "extension of Holder's theorem"
and also cites Otto Holder's original paper which is
Holder: Mathematische Annalen 28 (1887) 1-13
and they also cite several other proofs which presumably are slicker than Holder's original proof, but all are in German, French, or Russian except for
E.Moore: Mathematische Annalen 48 (1897) 49-74.