Method on @sym: sinc (x) ¶

Symbolic normalized sinc function.

The normalized sinc function is defined by

syms x
rewrite (sinc (x), 'sin')
  ⇒ (sym)
      ⎧sin(π⋅x)
      ⎪────────  for π⋅x ≠ 0
      ⎨  π⋅x
      ⎪
      ⎩   1       otherwise

Caution, the notation sinc is also commonly used to represent the unnormalized sinc function sin(x)/x.

Further examples:

rewrite (sin (x)/x, 'sinc')
  ⇒ ans = (sym)
           ⎛x⎞
       sinc⎜─⎟
           ⎝π⎠

rewrite (sin (pi*x)/(pi*x), 'sinc')
  ⇒ ans = (sym) sinc(x)

syms x nonzero
simplify (diff (sinc (x)))
  ⇒ ans = (sym)
       cos(π⋅x)   sin(π⋅x)
       ──────── - ────────
          x            2
                    π⋅x

See also: sinc.

Package: symbolic