Sextic Equation

The general sextic polynomial equation

$$x^6+a_5x^5+a_4x^4+a_3x^3+a_2x^2+a_1x+a_0=0$$

can be solved in terms of Hypergeometric Functions in one variable using Klein's approach to solving the Quintic Equation.

See also Cubic Equation, Quadratic Equation, Quartic Equation, 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.