Chieh-Lei Wong | Searcharxiv

arXiv2021

On the elegance of Ramanujan's series for $π$

Re presenting the traditional proof of Srinivasa Ramanujan's own favorite series for the reciprocal of $π$ :\begin{equation}\frac{1}π = \frac{\sqrt{8}}{9801} \sum_{n=0}^{+\infty} \frac{(4n)!}{(n!)^4} \frac{1103 + 26390n}{396^{4n}} \; \text{,}\end{equation}as well as several other examples of Ramanujan's infinite series. As a matter of fact, the derivation of such formulae has involved specialized knowledge of identities of classical functions and modular functions.

math.NT↗

arXiv2014

On the lack of compactness on stratified Lie groups

In $\mathbb{R}^d$, the characterization of the \mbox{lack of compactness of the continuous Sobolev injection $ \mathring{H}^s \hookrightarrow L^p $}, with $ \displaystyle{\frac{s}{d} + \frac{1}{p} = \frac{1}{2}} $ and $\displaystyle{0

math.AP↗