Band emission

Band emission, is the fraction of the total emission from a blackbody that is in a certain wavelength interval or band. For a prescribed temperature, T and the spectral interval from 0 to λ, is the ratio of the total emissive power of a black body from 0 to λ to the total emissive power over the entire spectrum.

${\displaystyle F_{0,\lambda }={\frac {\int _{0}^{\lambda }E_{\lambda ,b}d\lambda }{\int _{0}^{\infty }E_{\lambda ,b}d\lambda }}={\frac {\int _{0}^{\lambda }E_{\lambda ,b}d\lambda }{\sigma T^{4}}}=\int _{0}^{\lambda T}{\frac {E_{\lambda ,b}}{\sigma T^{5}}}d(\lambda T)=f(\lambda T)}$