# Infintite product true or not

Werg22
Is this true?

f(x)=sin(x)=x(x-2pi)(x-4pi)(x-6pi)...

edit:

f(x)=sin(x)=x(x-pi)(x-2pi)(x-3pi)(x-4pi)...

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Homework Helper
It doesn't seem right to me, try x = 2pi.

Werg22
Sorry I did a mistake. I meant sin(x).

Homework Helper
Try x = pi.

Werg22
I'm affraid I do not see what you mean... the serie is infinite...

Homework Helper
No, your infintite product does not even converge.

Infinite product form for sine:

$$\sin(x)=x\prod_{n=1}^{\infty}\left(1-\frac{x^2}{(\pi n)^2} \right)$$

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Homework Helper
Werg22 said:
I'm affraid I do not see what you mean... the serie is infinite...
I was trying to point out that sin(pi) = 0 but your serie would never go to 0.

Werg22
Sorry what I really meant is f(x)=sin(x)=x(x-pi)(x-2pi)(x-3pi)(x-4pi)...

Really sorry.