Wien's displacement law gives the frequency (or wavelength) at which the Planck law has the maximum specific intensity. Take the derivative with respect to frequency to find the extremum of the specific intensity

(1)

where h is Planck's constant, c is the speed of light, k is Boltzmann's constant, and T is the temperature. Solving,

	(2)

so

(3)

Let

(4)

and solve

(5)

This cannot be solved analytically using standard special functions of mathematical physics, but can be solved in terms of the Lambert's W-Function as

(6)

which has numerical solution is .

Planck Law