Question

Infinite product $\prod_k (1-z/a_k)(1-z/b_k)^{-1}$ converges uniformly on compacts of$\{\mathbb Im z>0\}$ and is Herglotz

score 287 · Answer 1 · 2016-01-12 19:26:32

287

Views

Infinite product $\prod_k (1-z/a_k)(1-z/b_k)^{-1}$ converges uniformly on compacts of$\{\mathbb Im z>0\}$ and is Herglotz

Published on 12 Jan 2016 - 19:26

score 313 · Answer 2 · 2026-03-27 00:57:59

313

Views

Paradox: Summation of natural logarithms

Published on 27 Mar 2026 - 0:57

score 183 · Answer 3 · 2016-01-21 12:27:18

183

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Show that $f(x^a) = a f(x) $ and $f(x y) = f(x) + f(y)$

Published on 21 Jan 2016 - 12:27

score 1k · Answer 4 · 2016-01-26 08:44:40

1k

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When An Infinite Product Topology Is Hausdorff?

Published on 26 Jan 2016 - 8:44

score 406 · Answer 5 · 2026-03-26 14:33:04

406

Views

Infinite exponentials

Published on 26 Mar 2026 - 14:33

score 51 · Answer 6 · 2016-01-30 23:22:09

51

Views

Alternative proof of $\prod_{n=1}^{+\infty}\frac{e^{it/2^n}+1}{2}=\frac{e^{it}-1}{it}$

Published on 30 Jan 2016 - 23:22

score 74 · Answer 7 · 2016-02-02 04:50:15

74

Views

Show $\prod_{n=1}^\infty 1 + \frac{-\left( 1 + z \right)}{n^2 + \left( 1 - n^2 \right) z}$ has no analytic extension past the unit disk

Published on 02 Feb 2016 - 4:50

score 72 · Answer 8 · 2026-03-31 03:45:42

72

Views

Finding an Entire function with $f(n \text{ln}(n)) = 0$ for $n \in \mathbb{N}$

Published on 31 Mar 2026 - 3:45

score 443 · Answer 9 · 2016-02-04 01:58:22

443

Views

Name of $\prod_{n = 1}^{\infty}n = 1 \times 2 \times 3 \times 4 \times 5 \times \cdots$

Published on 04 Feb 2016 - 1:58

score 113 · Answer 10 · 2016-02-05 01:57:48

113

Views

When is the limit of an infinite product equal to the infinite product of the limit?

Published on 05 Feb 2016 - 1:57

score 49 · Answer 11 · 2016-02-06 10:01:02

49

Views

Is there any identity for this series?

Published on 06 Feb 2016 - 10:01

score 1k · Answer 12 · 2026-03-29 18:13:36

1k

Views

Why don't infinite sums make any sense?

Published on 29 Mar 2026 - 18:13

score 207 · Answer 13 · 2016-02-08 13:26:43

207

Views

"Convergence"/"Divergence" of $\prod_{n=1}^\infty (1 - \gamma_n)$

Published on 08 Feb 2016 - 13:26

score 46 · Answer 14 · 2016-02-10 15:53:08

46

Views

Prove that if $0\le p_n \lt 1$ and $S:=\sum p_n \lt 1$, then $\Pi (1-p_n) \ge 1-S$.

Published on 10 Feb 2016 - 15:53

score 233 · Answer 15 · 2016-02-11 00:15:21

233

Views

Suppose $a_n>0$ for $n\in \mathbb{N}$. Prove that $\prod_{n=1}^\infty (1+a_n)$ converges if and only if $\sum_{n=1}^\infty a_n<\infty$.

Published on 11 Feb 2016 - 0:15

List Question

Infinite product $\prod_k (1-z/a_k)(1-z/b_k)^{-1}$ converges uniformly on compacts of$\{\mathbb Im z>0\}$ and is Herglotz

Paradox: Summation of natural logarithms

Show that $f(x^a) = a f(x) $ and $f(x y) = f(x) + f(y)$

When An Infinite Product Topology Is Hausdorff?

Infinite exponentials

Alternative proof of $\prod_{n=1}^{+\infty}\frac{e^{it/2^n}+1}{2}=\frac{e^{it}-1}{it}$

Show $\prod_{n=1}^\infty 1 + \frac{-\left( 1 + z \right)}{n^2 + \left( 1 - n^2 \right) z}$ has no analytic extension past the unit disk

Finding an Entire function with $f(n \text{ln}(n)) = 0$ for $n \in \mathbb{N}$

Name of $\prod_{n = 1}^{\infty}n = 1 \times 2 \times 3 \times 4 \times 5 \times \cdots$

When is the limit of an infinite product equal to the infinite product of the limit?

Is there any identity for this series?

Why don't infinite sums make any sense?

"Convergence"/"Divergence" of $\prod_{n=1}^\infty (1 - \gamma_n)$

Prove that if $0\le p_n \lt 1$ and $S:=\sum p_n \lt 1$, then $\Pi (1-p_n) \ge 1-S$.

Suppose $a_n>0$ for $n\in \mathbb{N}$. Prove that $\prod_{n=1}^\infty (1+a_n)$ converges if and only if $\sum_{n=1}^\infty a_n<\infty$.

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