Sextic Equation
The general sextic 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 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.
See also
Cubic Equation, Quadratic Equation, Quartic Equation, Quintic EquationExplore with Wolfram|Alpha
WolframAlpha
More things to try:
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.Referenced on Wolfram|Alpha
Sextic EquationCite this as:
Weisstein, Eric W. "Sextic Equation." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SexticEquation.html