This site is supported by donations to The OEIS Foundation.

# Heaviside step function

The Heaviside step function of ${\displaystyle \scriptstyle x\,}$ is defined as
${\displaystyle H(x)\equiv {\frac {\operatorname {sgn}(x)+1}{2}}={\begin{cases}0&{\text{if }}x<0,\\{\frac {1}{2}}&{\text{if }}x=0,\\1&{\text{if }}x>0.\end{cases}}}$