Frequency form of Wien's displacement law
= Frequency form of Wien's displacement law
{title2=$\nu_{\max}/T=x_*k_B/h,\quad x_*=2.821439\ldots$}
For the frequency version of <Planck law>, differentiating $x^3/(e^x-1)$ gives $3(1-e^{-x})=x$ at its nonzero maximum. Here $x=h\nu/(k_BT)$, 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.