Question

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

score 286 · Answer 1 · 2026-04-15 12:17:04

286

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

Published on 15 Apr 2026 - 12:17

score 103 · Answer 2 · 2026-05-10 16:21:01

103

Views

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

Published on 10 May 2026 - 16:21

score 183 · Answer 3 · 2026-05-10 16:14:49

183

Views

Is this zeta-type function meromorphic?

Published on 10 May 2026 - 16:14

score 300 · Answer 4 · 2026-04-17 06:27:01

300

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 17 Apr 2026 - 6:27

score 1.3k · Answer 5 · 2026-04-15 23:32:26

1.3k

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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 15 Apr 2026 - 23:32

score 236 · Answer 6 · 2026-04-15 11:13:47

236

Views

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

Published on 15 Apr 2026 - 11:13

score 140 · Answer 7 · 2026-04-13 23:02:19

140

Views

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

Published on 13 Apr 2026 - 23:02

score 146 · Answer 8 · 2026-04-10 19:33:19

146

Views

How can I show that this infinite product is nonzero?

Published on 10 Apr 2026 - 19:33

score 977 · Answer 9 · 2026-04-17 14:14:05

977

Views

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

Published on 17 Apr 2026 - 14:14

score 49 · Answer 10 · 2026-05-10 20:44:03

49

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 10 May 2026 - 20:44

score 95 · Answer 11 · 2026-04-13 13:52:51

95

Views

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

Published on 13 Apr 2026 - 13:52

score 2k · Answer 12 · 2026-04-14 08:19:34

2k

Views

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

Published on 14 Apr 2026 - 8:19

score 224 · Answer 13 · 2026-04-17 07:45:54

224

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 17 Apr 2026 - 7:45

score 2.6k · Answer 14 · 2026-04-15 07:25:26

2.6k

Views

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

Published on 15 Apr 2026 - 7:25

score 32 · Answer 15 · 2026-04-17 12:05:58

32

Views

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

Published on 17 Apr 2026 - 12:05

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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