ABSTRACT
This chapter explains Rayleigh–Jeans and Wien well-known approximations together with a number of other lesser known approximations that have been developed to approximate Planck's law. It also explains the problem of the accurate numerical evaluation of the blackbody fractional function of the first kind. The Wilhelm Carl Werner Otto Fritz Franz Wien approximation only applies where Wien's approximation is valid, it giving a slightly improved correction to the result found using Wien's law alone. While the logarithmic corrected form for Wien's law may be more accurate than either the Wien or the extended Wien approximations, as it involves function composition between exponentials, computationally it cannot be said to be very efficient for the gain in accuracy made. At first sight the computational effort required in using the method may seem large as values for the abscissae which require finding roots to the Laguerre polynomials and the corresponding weights are needed.
