Is there a closed form for $$\prod_{k=1}^n \cos(kx)$$ where $n>0$ is an integer?
This was proposed as $\prod_{k=1}^n a^k+\overline{a^k}$ where $a$ is a complex number, in the book of Claude Deschamps and Andre Warusfel (a French book).
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yes there is a closed form which conains the Pochhammer-function – Dr. Sonnhard Graubner Sep 04 '15 at 21:59
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Try to see this thread https://math.stackexchange.com/questions/3971805/proving-the-formula-for-%24%5Cprod_%7Bk%3D1%7D%5En-%5Ccos%28kx%29%24. You can find more on SearchOnMath. – José C Ferreira Mar 10 '22 at 18:27