Thu Mar 14 18:47:03 EDT 2013

Direct computation of 2D series

These are all interesting problems, but not sure if it is useful to
solve them.  There might be a simpler way to compute the 2D Taylor
series directly through differentials (autodiff).

( I'm thinking that diff is more work since there are more terms to
compute -- the tensors with partial derivatives -- but maybe the same
explosion happens for the function composition of sequences.  A
serious case of bad intuition here.. )

But... for 2 variables this isn't really such an explosion, is it?

0 f
1 f_x f_y
2 f_xx f_xy f_yy
3 f_xxx f_xxy f_xyy f_yyy

Still not convinced this will work for exp((P1 - log(p0)) / N).
Somehow not explicitly using the fact that P1 - log(p0) is small seems
to be be wrong, i.e. nothing special.  Somewhere, some cancelling is
going on eventually, but in what way?