Then w(z0)+w(z1)+... is your metarhizogenous function. (1-w(z0))(1-w(z1))(1-w(z2)).. also works. The trick is that since zn converges to a root of w, w(zn) converges to zero.
To build a metarhizogenous function you need: a. An iterative rootfinding method (Steffensens, Householder's, Newton's, etc.) and a b. function on the complex plane w(z) If for some point z0, the rootfinding method produces z1, z2,..
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