# Questions tagged [analytic-continuation]

For questions related to analytic continuation

541 questions
Filter by
Sorted by
Tagged with
25 views

### How do we prove this nested radical solution?

I’m submitting this question because my previous one was perhaps too verbose and did not get the point very quickly. A well known $\sqrt{2}$ nested radical has the following solutions as found in the ...
15 views

### A Nested Radical Arising from a Nonlinear Recurrence

I have been looking into analytic continuation of regular recurrence relations into the negative, real, and complex domains ($\mathbb{N} \mapsto \mathbb{Z}, \mathbb{R},\mathbb{C}$). In doing so, we’ve ...
61 views

### Prove that this limit is $-2$, which is a trivial zero of the Riemann zeta function.

The numerical evaluation of this formula works in Mathematica. Let: $$s=1$$ and truncate, at some large number, the limit involving the Harmonic numbers: $$f(x)= \lim_{m \rightarrow \infty}H_{m}^{x}$$ ...
13 views

181 views

### Numerical analytic continuation for $\tanh$-like function
I have a class of functions $f(z) \in \mathcal{F}$ of which I know the Taylor series at $z=0$ up to some free to choose order $N$. I am trying to numerically estimate the value of $f(z)$ outside its ...