1

x<0

d/dx(θ(x)) = piecewise | 0 | x!=0 indeterminate | (otherwise)

integral θ(x) dx = x θ(x) + constant

max{θ(x)} = 1 for x>=0

min{θ(x)} = 0 for x<0

lim_(x->-∞) θ(x) = 0

lim_(x->∞) θ(x) = 1

θ(x) = θ(x) for x!=0

θ(x) = θ(x_1, x_2, ..., x_n) for (x_1 = x and n = 1)

θ(x) = θ(x_1, x_2, ..., x_n) for (x_1 = x and x!=0 and n = 1)

θ(x) = (1 + sgn(x))/2 for (x element R and x!=0)

θ(x) = 1/2 + (2 sum_(k=0)^∞ sin(x + 2 k x)/(1 + 2 k))/π for -π

θ(x) = (lim_(ε->0) 1/ε integral_(-x)^∞ e^(-t^2/ε^2) dt)/sqrt(π)

θ(x) = (lim_(ε->0) integral_(-∞)^x sin(t/ε)/t dt)/π

θ(x) = (i lim_(ε->0) integral_(-∞)^∞ e^(-i t x)/(t + i ε) dt)/(2 π)