Using a Tschirnhausen transformation, the principal quintic form can be transformed to the one-parameter form w^5 - 10c w^3 + 45c^2 w - c^2 = 0 named after Francesco Brioschi (1824-1897) and which is important to the Klein's solution of the general quintic in terms of hypergeometric functions (Doyle and McMullen).

principal quintic form | quintic equation | Tschirnhausen transformation