Sextic Equation

The general sextic equation

can be solved in terms of Kampé de Fériet functions, and a restricted class of sextics can be solved in terms of generalized hypergeometric functions in one variable using Klein's approach to solving the quintic equation.

REFERENCES:

Coble, A. B. "The Reduction of the Sextic Equation to the Valentiner Form--Problem." Math. Ann. 70, 337-350, 1911a.

Coble, A. B. "An Application of Moore's Cross-Ratio Group to the Solution of the Sextic Equation." Trans. Amer. Math. Soc. 12, 311-325, 1911b.

Cole, F. N. "A Contribution to the Theory of the General Equation of the Sixth Degree." Amer. J. Math. 8, 265-286, 1886.