structural:expansion
Use in probability

Viewing the rectangular function as a probability density function, it is a special case of the continuous uniform distribution with a = − 1 / 2, b = 1 / 2. {\displaystyle a=-1/2,b=1/2.} The characteristic function is

φ (k) = sin (k / 2) k / 2, {\displaystyle \varphi (k)={\frac {\sin(k/2)}{k/2}},}

and its moment-generating function is

M (k) = sinh (k / 2) k / 2, {\displaystyle M(k)={\frac {\sinh(k/2)}{k/2}},}

where sinh (t) {\displaystyle \sinh(t)} is the hyperbolic sine function.