08/25/2009, 09:39 PM
We may also talk about different things.
You talk about continuing the islog to points outside the convergence radius.
But I talk about possibly different islogs (or isexps) that occur when developing the Carleman matrix at different points of the original function.
So the isexp@0.5 is perhaps not equal to the isexp@-1 and may hence also have different singularities, but perhaps they have very close singularities, who knows.
But in this line: When you continued the islog to the right (possibly several times), what happened with the convergence radius? Did it shrink? Are there more singularities of the islog (note that I previously talked about the singularities of the isexp) than just both primary fixed points?
I think in Henrici "Applied and computational complex analysis" there are error bounds for the continuation. If I remember right the more iterative steps you do for the continuation the more the size of the original development must increase. But then you can get the transposed coefficients inside arbitrary error bounds.
You talk about continuing the islog to points outside the convergence radius.
But I talk about possibly different islogs (or isexps) that occur when developing the Carleman matrix at different points of the original function.
So the isexp@0.5 is perhaps not equal to the isexp@-1 and may hence also have different singularities, but perhaps they have very close singularities, who knows.
But in this line: When you continued the islog to the right (possibly several times), what happened with the convergence radius? Did it shrink? Are there more singularities of the islog (note that I previously talked about the singularities of the isexp) than just both primary fixed points?
I think in Henrici "Applied and computational complex analysis" there are error bounds for the continuation. If I remember right the more iterative steps you do for the continuation the more the size of the original development must increase. But then you can get the transposed coefficients inside arbitrary error bounds.