Question Number 117144 by cantor last updated on 09/Oct/20
$$\boldsymbol{{S}}_{\boldsymbol{{n}}} =\underset{\boldsymbol{{k}}=\mathrm{1}} {\overset{\boldsymbol{{n}}} {\prod}}\boldsymbol{{cos}}\left(\boldsymbol{{kx}}\right)=?????? \\ $$$$\boldsymbol{{please}}\:\boldsymbol{{help}} \\ $$
Answered by Olaf last updated on 10/Oct/20
$$ \\ $$$$\mathrm{No}\:\mathrm{general}\:\mathrm{formula}\:\mathrm{for}\:\mathrm{that}\:! \\ $$$$ \\ $$$$\mathrm{Some}\:\mathrm{formulas}\:\mathrm{exist}\:\mathrm{for}\:\mathrm{particular} \\ $$$$\mathrm{values}\:\mathrm{of}\:{x}\:\mathrm{or}/\mathrm{and}\:\mathrm{for}\:{n}\:=\:\infty. \\ $$