peak m=1 (mu=3/2): 0.8198325579; m=2: 0.8111736168; m=3: 0.8073952942; m=5000: 0.7978912092; sqrt(2/pi) = 0.7978845608
peaks strictly decreasing for m = 1..5000: True; all < 0.82: True
direct check of the mean-deviation formula at mu = 1.5, 2.7: -1.97e-31, -7.89e-31
min of 2 sqrt(x) e^(-x) on [0.325, 0.675]: 0.82380793 (unimodal, peak at 1/2)
