I made it with the following Gnuplot code:

# set the output
set terminal svg
set output "hermite_poly.svg"

set title "Hermite Polynomials"

# axis properties
set xrange [-3.5:6.5]
set yrange [-10:20]
set xzeroaxis linetype -1 linewidth 0.5
set yzeroaxis linetype -1 linewidth 0.5
set xlabel "x"
set ylabel "H_n (x)"
plot 1 ti "n = 0" with lines linewidth 2,\
     x ti "n = 1" with lines linewidth 2,\
     x**2-1 ti "n = 2" with lines linewidth 2,\
     x**3-3*x ti "n = 3" with lines linewidth 2,\
     x**4-6*x**2+3 ti "n = 4" with lines linewidth 2,\
     x**5-10*x**3+15*x ti "n = 5" with lines linewidth 2