What version of sinc function to use ? (With additional factor of $\pi$ or not.)
Some time ago, on our sister site math.SE, I wrote about this issue regarding the two different definitions of the sinc function.  Here is a slightly modified version of that answer for the benefit of those who prefer to just stay on dsp.SE.


  In the engineering literature, those who define the Fourier transform as
  $$X(\omega) = \int_{-\infty}^{\infty} x(t)\exp(-j\omega t)\ \mathrm dt$$
  tend to use the unnormalized version $\frac{\sin(x)}{x}$, while those who define the Fourier
  transform as
  $$X(f) = \int_{-\infty}^{\infty} x(t)\exp(-j2\pi f t)\ \mathrm dt$$
  tend to use the normalized version $\frac{\sin(\pi x)}{\pi x}$.  My personal preference is for the
  normalized version because the zeroes of the function are the
  nonzero integers, but, like most people, I have learned to live
  with both definitions and figure out which one an author is using
  even if it is not explicitly stated. There are, of course, zealots
  who say that people who use the convention they do not happen
  to prefer are in a state of sin (or did I mean to say a state of sinc?)
  
  Incidentally, I would like to say that my preference for the
  definition of the sinc (or sine cardinal) function is
  $$\mathrm{sinc}(x) = \begin{cases}\frac{\sin(\pi x)}{\pi x}, &amp; x \neq 0,\\
1, &amp; x = 0,\end{cases}$$
  and not simply $\mathrm{sinc}(x) = \sin(\pi x)/(\pi x)$ the way the OP 
  and Wikipedia states it.


I do disagree with Fat32's didactic assertion that if sinc is not defined in a paper or book or on an exam or homework, then one should assume that it is the normalized version that is meant and proceed accordingly. In my experience, it is more commonly the case that if the frequency variable is $\omega$ (radians per second), then the unnormalized version is used while if the frequency variable is $f$ (Hertz), then the normalized version is used, but this is by no means a hard and fast rule that everyone follows.