formula

planck's law
2k^4/(h^3c^2)  T^4 x^3/(e^x-1) dx
x=h ν/(kT)

x             x/(1-e^(-x))
0            1
1.593    1.999534952
2.821    2.999616249  (max  ν)
3.920    3.999351512
4.965    4.999888979  (max λ)

Maxwell–Boltzmann distribution
2/pi^0.5 x^0.5 e^(-x) dx
x= E/(kT) = mv^2/(2kT)