Frobenius–Padé approximants of |x||x|

We construct the Frobenius–Padé approximants of the function |x||x| in (−1,1)(−1,1) for the Chebyshev weight. These rational functions are linked with the Frobenius–Padé approximants of the function x in (0,1)(0,1). We prove geometric convergence of the approximants of |x||x| in C∖{z:ℜ(z)=0}C∖{z:ℜ(z)=0}.