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Results tagged with cv.complex-variables
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user 113397
Complex analysis, holomorphic functions, automorphic group actions and forms, pseudoconvexity, complex geometry, analytic spaces, analytic sheaves.
30
votes
1
answer
4k
views
Proof of "Possible new series for $\pi$" without use of physics
Related post: The post Possible new series for $\pi$ is about whether the identity is new, so to avoid confusion I was advised to ask this question separately.
I am looking for a proof of the follo …
- 1,459
9
votes
1
answer
222
views
Is $(m,n)=(2,3)$ the only solution to $\sum_\limits{k \in\Bbb Z}\frac1{(W_k(x)+1)^m}=\sum_\l...
From discussions 1, 2, @HenriCohen wrote a paper on Lambert $W$-Function Branch Identities which includes identities such as $$\sum_\limits{k
\in\Bbb Z}\frac1{(W_k(x)+1)^2}=\sum_\limits{k
\in\Bbb Z}\f …
- 1,459
5
votes
1
answer
357
views
Is there a meaningful interpretation of an $L^i$-space?
Do complex-normed spaces exist? Is there an extension of $p$-norms to $p\in\Bbb C\setminus\Bbb R$?
A while ago I thought of extending $L^p$-spaces to the complex-normed setting. After some discussions …
- 1,459
4
votes
1
answer
183
views
Maximal increasing behaviour of $\sqrt{-\log x}\operatorname{Li}_{1/2}(x)$
This is an extension of a problem in mathematical biology. It appears that
For any $\varepsilon>0$, there exists an interval $I\subset(0,1)$ on which $\sqrt{-\log x}^{1+\varepsilon}\operatorname{Li}_ …
- 1,459
2
votes
New series for $\pi$ from string theory
It is unlikely $S(1)$ has a closed form.
We have \begin{align}S(1)&=4\sum_{k\ge1}(-1)^k\binom{-1/(4k)}k\frac{2k}{2k+1}\end{align} and (substituting $\lambda=0$ in the original Saha-Sinha formula for $ …
- 1,459