The gnuplot (Version 5.4 Windows patchlevel 5) for the function described in the first line below does not work, the second one does. What is going on?
plot [0:2] [0:4] f(x) = 1/2/(pi*d)**0.5*exp(-1*(1-x)**2/(4*d)), d = 0.0065, f(x)
#plot [0:2] [0:4] f(x) = 1/(2*(pi*d)**0.5)*exp(-1*(1-x)**2/(4*d)), d = 0.0065, f(x)
The above two lines are the narrowed down version from several alternatives involving sqrt instead of **2.
This is the "everlasting" gnuplot pitfall: integer division, i.e. 1/2=0. Use for example f(x) = 1.0/2/... instead.