By a "graph that shows the convergence of the series" you mean like a graph of partial sums? Also, I could try a root test or ratio test but I think to make it really good I'll need more terms... Is there a general algorithm or formula to generate those polynomials in the regular iteration series?

EDIT: I just saw the paper and there appears to be a recurrence formula on page 8 but am a little confused by the notation. Specifically, what's supposed to be? nth Taylor coefficient of m iterations of g? But we have not yet determined g, so how can we iterate?

EDIT: I just saw the paper and there appears to be a recurrence formula on page 8 but am a little confused by the notation. Specifically, what's supposed to be? nth Taylor coefficient of m iterations of g? But we have not yet determined g, so how can we iterate?