I'm reseaching a problem that lead me to evaluating the product $$\prod\limits_{k=1}^{[n/4]} \tan \dfrac{k\pi}{n}=?,$$ I can evaluate $$\prod\limits_{k=1, k\neq \frac{n}{2}}^{n}\vert \tan \dfrac{k\pi}{n}\vert=\left\{ \begin{array}{l}n, n \text{ is odd} \\ 1, n\text{ is even} \end{array}\right.,$$ but i can't solve the above product, please. Thanks a ton.
Asked
Active
Viewed 92 times
4
-
What do you get for the first few cases? – GEdgar Jun 30 '17 at 13:45
-
The product looks very ugly :-/ when opened! – Math-fun Jun 30 '17 at 15:12
-
I tried the first few cases, the product is irrational numbers but i wanna try to write the result neatly and exactly so as run with low condition number in matlab :( – J.Simpson Jul 01 '17 at 05:59