Wien's displacement law gives the frequency (or wavelength) at which the Planck law has the maximum specific intensity. Take the derivative Eric Weisstein's World of Math with respect to frequency to find the extremum of the specific intensity
where h is Planck's constant, c is the speed of light, k is Boltzmann's constant, and T is the temperature. Solving,
so
Let
and solve
This cannot be solved analytically using standard special functions of mathematical physics, but can be solved in terms of the Lambert's W-Function Eric Weisstein's World of Math as
which has numerical solution is
