Well known and conventional defintion of Heaviside function is
H(x) = 0, x < 0 H(x) = 1/2, x = 0 H(x) = 1, x > 0
Mathematica uses instead unconventional "unit step" for its $HeavisideTheta[x] $ function
S(x) = 0, x < 0 S(x) = 1, x > 0
How to use in Mathematica proper Heaviside function with normal definiton $H(x)$?