Divergent Series and Analytical Continuation (LONG post)

[JmsNxn]

  

Also, you are very much discussing the first step of the little circle method here.

The second part is to "estimate" the half circles you have drawn, and the arcs of the circle.

For Caleb's function \(f(x)\)--we don't have to do this because we are defined outside of the unit circle. But when we are only defined within the unit disk, the only way to do this is to estimate the circle and the arcs for the partial terms.

If that makes sense