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Results tagged with cv.complex-variables
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user 17218
Complex analysis, holomorphic functions, automorphic group actions and forms, pseudoconvexity, complex geometry, analytic spaces, analytic sheaves.
1
vote
0
answers
105
views
sum involving Riemann zeta function
In my work arose the following series:
$$g(s) = \sum_{n = 0}^\infty \frac{\log(\zeta(n+2))}{n+2}s^{n}.$$
It has radius of convergence $2$ and converges for $|s| \leq 2$ except at $s = 2$. I'm wonderi …
- 4,985
1
vote
1
answer
166
views
Analyzable functions and accelero-summation
Is there a complete and rigorous, yet concise, definition of what an analyzable function is, along with the related notion of accelero-summation, both in the sense of Écalle? All of the definitions I …
- 4,985
1
vote
0
answers
93
views
Bound for truncation error of continued fraction for $E_1(z)$
Let $z \in \mathbb C \setminus(-\infty,0)$. It is known that
$$E_1(z) = \cfrac{e^{-z}}{z+\cfrac{1}{1+\cfrac{1}{z+\cfrac{2}{1+\cfrac{2}{z+\cfrac{3}{1+\cdots}}}}}}.$$
For example, see http://functions. …
- 4,985
7
votes
1
answer
515
views
continued fraction for logarithmic integral
Does the logarithmic integral function $\operatorname{li}(x)$ have the continued fraction expansion
$$\operatorname{li}(x) = \cfrac{x}{\log x -1 -{}} \ \cfrac{1}{\log x -3 -{}} \ \cfrac{4}{\log x - …
- 4,985
6
votes
Algorithm for Weierstrass Preparation Theorem for Formal Power Series
If you're still interested in the answer to this...I also needed an explicit algorithm for calculating associated Weierstrass polynomials and provide two such algorithms in http://arxiv.org/abs/1107.4 …
- 4,985