Nyquist–Shannon sampling theorem-proof

Question

I don't understand the last derivation. Why there isn't $\pi$ in the sinc function? I would think that it is a mistake , but even in the Wikipedia it appears without $\pi$.

https://en.wikipedia.org/wiki/Nyquist%E2%80%93Shannon_sampling_theorem

Answer 1

According to some conventions, the $\mathrm{sinc}$ function has a $\pi,$ in it, i.e. $$ \mathrm{sinc}(x) = \frac{\sin(\pi x)}{\pi x}$$ instead of $$\mathrm{sinc}(x) = \frac{\sin(x)}{x}$$