Question

How to use Euler formula to prove the following conclusion？

score 77 · Answer 1 · 2020-03-31 11:57:28

77

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How to use Euler formula to prove the following conclusion？

Published on 31 Mar 2020 - 11:57

score 555 · Answer 2 · 2020-04-01 05:37:10

555

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Find value of $\prod_{k=0}^{2^{1999}}\left(4\sin^2\left(\frac{k\pi}{2^{2000}}\right)-3\right)$

Published on 01 Apr 2020 - 5:37

score 118 · Answer 3 · 2020-04-01 11:18:30

118

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When the product $|\prod_{k=1}^n(1-z^k)|$ tends to infinity?

Published on 01 Apr 2020 - 11:18

score 44 · Answer 4 · 2020-04-04 23:30:35

44

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If $F(n)$ is the unique number of arranging $n \ge 1$ unique items, prove inductively that $F(n) = n!$

Published on 04 Apr 2020 - 23:30

score 331 · Answer 5 · 2020-04-08 09:09:34

331

Views

Borel sigma algebra on uncountable product and product sigma-algebra

Published on 08 Apr 2020 - 9:09

score 315 · Answer 6 · 2020-04-09 16:08:43

315

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Show convergence of infinite product

Published on 09 Apr 2020 - 16:08

score 47 · Answer 7 · 2020-04-11 01:12:39

47

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Limit of the infinite product

Published on 11 Apr 2020 - 1:12

score 79 · Answer 8 · 2020-04-13 05:05:04

79

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Calculating $\prod\limits_{k=0}^\infty(1+{\rm e}^{-(2k+1)\pi})$

Published on 13 Apr 2020 - 5:05

score 150 · Answer 9 · 2020-04-13 15:09:36

150

Views

Prove $\prod_{n \in \Bbb{N} } \left(\frac{1-q^n}{1+q^n}\right)^{(-1)^n} = \sum_{n \in \Bbb{Z}} q^{n^2}$

Published on 13 Apr 2020 - 15:09

score 650 · Answer 10 · 2020-04-15 05:04:55

650

Views

When is the Infinite product of continuous functions a continuous function? Assume that the product is convergent.

Published on 15 Apr 2020 - 5:04

score 389 · Answer 11 · 2020-04-16 16:31:15

389

Views

Infinite product for sin z

Published on 16 Apr 2020 - 16:31

score 53 · Answer 12 · 2020-04-16 16:51:18

53

Views

An infinite product obtained by taking every third term from the Wallis product. Is it new?

Published on 16 Apr 2020 - 16:51

score 70 · Answer 13 · 2020-04-17 16:20:51

70

Views

What value does $\prod_{n=0}^\infty 1+{1\over x^n}$ converge to?

Published on 17 Apr 2020 - 16:20

score 158 · Answer 14 · 2020-04-18 01:18:52

158

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how to calculate $ \prod_{n=1}^\infty\left(1\pm q^{2n-1}\right), \prod_{n=1}^\infty\left(1\pm q^{2n}\right)$

Published on 18 Apr 2020 - 1:18

score 130 · Answer 15 · 2020-04-18 13:19:30

130

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Computing $\lim_{n\to\infty} \prod_{k=1}^n(1-\frac{x^2k^{2\alpha}}{n^{2 \alpha+1}})$

Published on 18 Apr 2020 - 13:19

List Question

How to use Euler formula to prove the following conclusion？

Find value of $\prod_{k=0}^{2^{1999}}\left(4\sin^2\left(\frac{k\pi}{2^{2000}}\right)-3\right)$

When the product $|\prod_{k=1}^n(1-z^k)|$ tends to infinity?

If $F(n)$ is the unique number of arranging $n \ge 1$ unique items, prove inductively that $F(n) = n!$

Borel sigma algebra on uncountable product and product sigma-algebra

Show convergence of infinite product

Limit of the infinite product

Calculating $\prod\limits_{k=0}^\infty(1+{\rm e}^{-(2k+1)\pi})$

Prove $\prod_{n \in \Bbb{N} } \left(\frac{1-q^n}{1+q^n}\right)^{(-1)^n} = \sum_{n \in \Bbb{Z}} q^{n^2}$

When is the Infinite product of continuous functions a continuous function? Assume that the product is convergent.

Infinite product for sin z

An infinite product obtained by taking every third term from the Wallis product. Is it new?

What value does $\prod_{n=0}^\infty 1+{1\over x^n}$ converge to?

how to calculate $ \prod_{n=1}^\infty\left(1\pm q^{2n-1}\right), \prod_{n=1}^\infty\left(1\pm q^{2n}\right)$

Computing $\lim_{n\to\infty} \prod_{k=1}^n(1-\frac{x^2k^{2\alpha}}{n^{2 \alpha+1}})$

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