New Wallis- and Catalan-Type Infinite Products for $\pi ,e$, and $\sqrt{2+\sqrt{2}}$

Jonathan Sondow, Huang Yi

We generalize Wallis's 1655 infinite product for $\pi /2$ to one for $(\pi /K)\csc (\pi /K)$, as well as give new Wallis-type products for $\pi /4,2,\sqrt{2+\sqrt{2}},2\pi /3\sqrt{3},$ and other co…