Question

What is the infinite product of (primes^2+1)/(primes^2-1)?

score 1.3k · Answer 1 · 2016-03-23 09:12:49

1.3k

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What is the infinite product of (primes^2+1)/(primes^2-1)?

Published on 23 Mar 2016 - 9:12

score 78 · Answer 2 · 2016-03-26 20:30:40

78

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Zeroes of infinite product function?

Published on 26 Mar 2016 - 20:30

score 633 · Answer 3 · 2016-03-29 07:40:09

633

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Rearranging infinite product

Published on 29 Mar 2016 - 7:40

score 65 · Answer 4 · 2016-04-03 13:38:26

65

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How to prove the product representation of Baenes G-function?

Published on 03 Apr 2016 - 13:38

score 65 · Answer 5 · 2016-04-03 17:53:35

65

Views

Infinite expansion of difference of squares?

Published on 03 Apr 2016 - 17:53

score 445 · Answer 6 · 2016-04-04 09:21:47

445

Views

What is $2^{\frac{1}{4}}\cdot4^{\frac{1}{8}}\cdot8^{\frac{1}{16}}\cdot16^{\frac{1}{32}}\cdots\infty$ equal to?

Published on 04 Apr 2016 - 9:21

score 1.1k · Answer 7 · 2016-04-07 03:13:23

1.1k

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Interesting representation of $e^x$

Published on 07 Apr 2016 - 3:13

score 514 · Answer 8 · 2016-04-09 23:45:00

514

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Show $\cos \pi z=\prod\limits_{-\infty}^\infty \left(1-\frac{2z}{2n-1}\right) e^{\frac{2z}{2n-1}}$

Published on 09 Apr 2016 - 23:45

score 246 · Answer 9 · 2016-04-12 10:20:49

246

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If $a_n=\left(1-\frac{1}{\sqrt{2}}\right)\ldots\left(1-\frac{1}{\sqrt{n+1}}\right)$ then $\lim_{n\to\infty}a_n=?$

Published on 12 Apr 2016 - 10:20

score 220 · Answer 10 · 2016-04-13 09:34:26

220

Views

Prove that $\lim_{\ r\ \to \ \infty} \dfrac{r! r^x}{x(x+1)(x+2) \dots (x+r)} = \int_{0}^{\infty} t^{x-1} e^{-t} dt $

Published on 13 Apr 2016 - 9:34

score 6k · Answer 11 · 2016-04-13 13:18:07

6k

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Proving a result in infinite products: $\prod (1+a_n)$ converges (to a non zero element) iff the series $\sum a_n$ converges

Published on 13 Apr 2016 - 13:18

score 3.7k · Answer 12 · 2016-04-13 19:38:29

3.7k

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Product of all numbers in a given interval $[n,m]$

Published on 13 Apr 2016 - 19:38

score 89 · Answer 13 · 2016-04-16 01:33:55

89

Views

Proof of Jacobi triple product by taking the limit

Published on 16 Apr 2016 - 1:33

score 255 · Answer 14 · 2016-04-20 09:38:03

255

Views

Evaluate this infinite product: $\prod_{n=3}^{\infty} \left(\;1-\frac{4}{n^2}\;\right)$

Published on 20 Apr 2016 - 9:38

score 79 · Answer 15 · 2026-03-29 19:10:07

79

Views

Understanding the expansion of product notation.

Published on 29 Mar 2026 - 19:10

List Question

What is the infinite product of (primes^2+1)/(primes^2-1)?

Zeroes of infinite product function?

Rearranging infinite product

How to prove the product representation of Baenes G-function?

Infinite expansion of difference of squares?

What is $2^{\frac{1}{4}}\cdot4^{\frac{1}{8}}\cdot8^{\frac{1}{16}}\cdot16^{\frac{1}{32}}\cdots\infty$ equal to?

Interesting representation of $e^x$

Show $\cos \pi z=\prod\limits_{-\infty}^\infty \left(1-\frac{2z}{2n-1}\right) e^{\frac{2z}{2n-1}}$

If $a_n=\left(1-\frac{1}{\sqrt{2}}\right)\ldots\left(1-\frac{1}{\sqrt{n+1}}\right)$ then $\lim_{n\to\infty}a_n=?$

Prove that $\lim_{\ r\ \to \ \infty} \dfrac{r! r^x}{x(x+1)(x+2) \dots (x+r)} = \int_{0}^{\infty} t^{x-1} e^{-t} dt $

Proving a result in infinite products: $\prod (1+a_n)$ converges (to a non zero element) iff the series $\sum a_n$ converges

Product of all numbers in a given interval $[n,m]$

Proof of Jacobi triple product by taking the limit

Evaluate this infinite product: $\prod_{n=3}^{\infty} \left(\;1-\frac{4}{n^2}\;\right)$

Understanding the expansion of product notation.

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