Frequency form of Wien's displacement law (${\nu }_{\max }/T=x_{\ast }{k}_B/h,x_{\ast }=2.821439\dots$)

For the frequency version of Planck law, differentiating $x^3/(e^x-1)$ gives $3(1-e^{-x})=x$ at its nonzero maximum. Here $x=h\nu /(k_{B}T)$, so the peak frequency is proportional to temperature. This peak differs from converting the peak of the wavelength version by $\nu =c/\lambda$, because spectral densities transform with a Jacobian.