Question

Solution to infinite product $\prod_{p-primes}^{\infty} \frac{p}{p-1}$

score 283 · Answer 1 · 2018-11-24 15:07:20

283

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Solution to infinite product $\prod_{p-primes}^{\infty} \frac{p}{p-1}$

Published on 24 Nov 2018 - 15:07

score 96 · Answer 2 · 2026-03-22 21:08:08

96

Views

Need someone to show me how the Zeta function is equal to Euler's product formula?

Published on 22 Mar 2026 - 21:08

score 180 · Answer 3 · 2026-03-25 05:58:58

180

Views

Is this zeta-type function meromorphic?

Published on 25 Mar 2026 - 5:58

score 297 · Answer 4 · 2018-11-30 06:56:17

297

Views

Show that $\int_0^1 \prod_{n\geq 1} (1-x^n) \, dx = \frac{4\pi\sqrt{3}\sinh(\frac{\pi}{3}\sqrt{23})}{\sqrt{23}\cosh(\frac{\pi}{2}\sqrt{23})}$

Published on 30 Nov 2018 - 6:56

score 1.3k · Answer 5 · 2018-11-30 15:05:28

1.3k

Views

Prove that $\prod_{i=1}^n (1+x_i/n) \sim \exp (\sum_{i=1}^n x_i/n)$ as $n\rightarrow\infty$?

Published on 30 Nov 2018 - 15:05

score 233 · Answer 6 · 2018-12-06 15:50:14

233

Views

If a product of polynomials converges, does some product of their zeros also converge?

Published on 06 Dec 2018 - 15:50

score 138 · Answer 7 · 2026-03-25 22:25:57

138

Views

Does the infinite product of the reciprocals of a decreasing (or increasing) function equal zero?

Published on 25 Mar 2026 - 22:25

score 143 · Answer 8 · 2018-12-10 19:22:03

143

Views

How can I show that this infinite product is nonzero?

Published on 10 Dec 2018 - 19:22

score 975 · Answer 9 · 2026-03-26 01:34:49

975

Views

Integral $\int_0^1 \frac{dx}{\prod_{n=1}^\infty (1+x^n)}$

Published on 26 Mar 2026 - 1:34

score 46 · Answer 10 · 2026-03-25 17:20:02

46

Views

Verifying that $ \prod_{j=1}^{\infty} \frac{1}{1-q^j} = \prod_{j=1}^{\infty} \frac{1}{(1-q^{2j-1})(1-q^{2j})}$

Published on 25 Mar 2026 - 17:20

score 92 · Answer 11 · 2018-12-23 06:17:17

92

Views

Demonstrating an equivalent formula for $\sin(x)/x$ using power series

Published on 23 Dec 2018 - 6:17

score 2k · Answer 12 · 2018-12-27 03:36:56

2k

Views

When does the tensor product distribute over an infinite direct product?

Published on 27 Dec 2018 - 3:36

score 221 · Answer 13 · 2018-12-30 10:47:11

221

Views

Evaluate $\frac{2}{\sqrt{2}}\cdot \frac{2}{\sqrt{2+\sqrt{2}}}\cdot \frac{2}{\sqrt{2+\sqrt{2+\sqrt{2}}}}\cdots$

Published on 30 Dec 2018 - 10:47

score 2.6k · Answer 14 · 2019-01-03 15:39:56

2.6k

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On calculating the limit of the infinite product $\prod_{k=3}^n (1-\tan^4\frac{\pi}{2^k})$

Published on 03 Jan 2019 - 15:39

score 27 · Answer 15 · 2019-01-10 15:13:54

27

Views

Methods for assigning values to infinite constructs (ex. sums, products)

Published on 10 Jan 2019 - 15:13

List Question

Solution to infinite product $\prod_{p-primes}^{\infty} \frac{p}{p-1}$

Need someone to show me how the Zeta function is equal to Euler's product formula?

Is this zeta-type function meromorphic?

Show that $\int_0^1 \prod_{n\geq 1} (1-x^n) \, dx = \frac{4\pi\sqrt{3}\sinh(\frac{\pi}{3}\sqrt{23})}{\sqrt{23}\cosh(\frac{\pi}{2}\sqrt{23})}$

Prove that $\prod_{i=1}^n (1+x_i/n) \sim \exp (\sum_{i=1}^n x_i/n)$ as $n\rightarrow\infty$?

If a product of polynomials converges, does some product of their zeros also converge?

Does the infinite product of the reciprocals of a decreasing (or increasing) function equal zero?

How can I show that this infinite product is nonzero?

Integral $\int_0^1 \frac{dx}{\prod_{n=1}^\infty (1+x^n)}$

Verifying that $ \prod_{j=1}^{\infty} \frac{1}{1-q^j} = \prod_{j=1}^{\infty} \frac{1}{(1-q^{2j-1})(1-q^{2j})}$

Demonstrating an equivalent formula for $\sin(x)/x$ using power series

When does the tensor product distribute over an infinite direct product?

Evaluate $\frac{2}{\sqrt{2}}\cdot \frac{2}{\sqrt{2+\sqrt{2}}}\cdot \frac{2}{\sqrt{2+\sqrt{2+\sqrt{2}}}}\cdots$

On calculating the limit of the infinite product $\prod_{k=3}^n (1-\tan^4\frac{\pi}{2^k})$

Methods for assigning values to infinite constructs (ex. sums, products)

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