On an inequality of a product function

Real Analysis
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Riemann
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Location: Melbourne, Australia

On an inequality of a product function

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Post by Riemann »

Let

$$f(x) = \sin x \sin (2x) \sin (4x) \cdots \sin (2^n x)$$

Prove that

$$\left| {f(x)} \right| \le \frac{2}{{\sqrt 3 }}\left| {f(\frac{\pi }{3})} \right|$$
$\displaystyle \sum_{n=1}^{\infty}\frac{1}{n^s}= \prod_{p \; \text{prime}}\frac{1}{1-p^{-s}}$
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