Seeking infinite product representations of $\pi$ (other than Wallis)

Question

I am looking for a list of as many representations of $\pi$ using "$\prod$" product notation; i.e., an infinite product for $\pi$. An example would be the Wallis product

$$\pi=4\prod_{n=1}^{\infty}\left(1-\frac{1}{\left(2n+1\right)^{2}}\right)$$

Do you know of any resources where I can find something like that?

It is well-known as Wallis product. Also it's proof is well-known. — MH.Lee, Oct 23 '21 at 12:31
@Nightflight, the OP clearly knows the name (they just didn't capitalize it). What they're asking for are other (presumably non-trivial) infinite products that produce $\pi$. — Barry Cipra, Oct 23 '21 at 12:44
Googling on "product representations of pi" took me to https://functions.wolfram.com/Constants/Pi/08/ShowAll.html among other sites. — Barry Cipra, Oct 23 '21 at 12:46

score 1 · Answer 1 · answered Oct 23 '21 at 13:05

Some product formulas for $\pi$ from this site:

1.) $(\frac{2 \times 2}{1 \times 3}) \times (\frac{4 \times 4}{3 \times 5}) \times (\frac{6 \times 6}{5 \times 7}) \times \cdots = \frac{\pi}{2}$

2.) Why this is equal to $\pi$?

3.) An infinite product for $\frac{\pi}{2}$

4.) How to prove $ \prod_{n=1}^{\infty} \left(1+\frac{2}{n}\right)^{(-1)^{n+1}n} \,= \frac{\pi}{2e}$

5.) Prove that ${\pi\over2}=\left({2\over1}\right)^{1\over2}\left({2^2\over 1\cdot3}\right)^{1\over 4} \cdots$

Seeking infinite product representations of $\pi$ (other than Wallis)

1 Answers1