11/07/2009, 08:17 AM

(11/07/2009, 12:23 AM)mike3 Wrote: By a "graph that shows the convergence of the series" you mean like a graph of partial sums?

Yes, yes, x-axis: n, y-axis: n-th partial sum.

Quote:Also, I could try a root test or ratio test but I think to make it really good I'll need more terms...

With root test the same: x-axis: n, y-axis: . The root-test should converge to something bigger than the distance from the development point to the perhaps-singularity.

Quote: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?In this draft integer-iteration is always denoted by , while power is as usual . depends only on values , . You can take the polynomial of g truncated to n, then take the m-th power and then get the coefficient at n.