# Two classes of explicitly solvable sextic equations

@inproceedings{Calogero2021TwoCO, title={Two classes of explicitly solvable sextic equations}, author={Francesco Calogero and F. Payandeh}, year={2021} }

The generic monic polynomial of sixth degree features 6 a priori arbitrary coefficients. We show that if these 6 coefficients are appropriately defined—in two different ways—in terms of 5 arbitrary parameters, then the 6 roots of the corresponding polynomial can be explicitly computed in terms of radicals of these parameters. We also report the 2 constraints on the 6 coefficients of the polynomial implied by the fact that they are so defined in terms of 5 arbitrary parameters; as well as the…

## 2 Citations

### Explicitly solvable algebraic equations of degree 8 and 9

- Mathematics
- 2021

The generic monic polynomial of degree N features N a priori arbitrary coefficients cm and N zeros zn . In this paper we limit consideration to N = 8 and N = 9 . We show that if the N —a priori…

### A solvable nonlinear autonomous recursion of arbitrary order

- Mathematics
- 2021

The initial-values problem of the following nonlinear autonomous recursion of order p ,

## References

### General Formulas for Solving Solvable Sextic Equations

- Mathematics
- 2000

Abstract Let G be a transitive, solvable subgroup of S6. We show that there is a common formula for finding the roots of all irreducible sextic polynomials f(x) ∈ Q[x] with Gal(f) = G. Moreover, once…