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?
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 ${\pi\over2}=\left({2\over1}\right)^{1\over2}\left({2^2\over 1\cdot3}\right)^{1\over 4} \cdots$