# Tagged Questions

2k views

### The unreasonable effectiveness of Pade approximation

I am trying to get an intuitive feel for why the Pade approximation works so well. Given a truncated Taylor/Maclaurin series it "extrapolates" it beyond the radius of convergence. But what I can't ...
653 views

### What is the theoretical interest of finding closed-form sols. of infinite series?

Hi, I was reading this when I came across Gourevitch's conjecture. My understanding is that solutions to these series are of practical interest. If one encounters such a series, being able to solve ...
280 views

### Evaluating a limit similar to the Euler constant

In the course of studying a certain complex-valued functional equation, I have had a need to evaluate the following limit: \gamma_\mathcal{T}=\lim_{n\to\infty}\left(-\frac{i}{2}\sum_{k=1}^n ...
I've come across this infinite series: $\sum_{n=0}^\infty x^{n^\alpha}$, with $0<x<1$ and $\alpha > 0$. Does this series have a name and/or is there a method for computing it (besides brute ...
I'm wondering if there is a way to approximate the first $M$ terms of a non-increasing $\ell^2$ sequence $\{c_n\}$ if we know $|c|_p^p = \sum c_n^p$ for $p=2,3,4,\dots$? I've tried truncating the ...