Author(s)

Sabaratnasingam Gnanarajan

Aruja & Arjun Pty Ltd., Sydney, Australia.

Planck’s radiation law provides an equation for the intensity of the electromagnetic radiation from a physical body as a function of frequency and temperature. The frequency that corresponds to the maximum intensity is a function of temperature. At a specific temperature, for the frequencies correspond to much less than the maximum intensity, an equation was derived in the form of the Lambert W function. Numerical calculations validate the equation. A new form of solution for the Euler’s transcendental equation was derived in the form of the Lambert W function with logarithmic argument. Numerical solutions to the Euler’s equation were determined iteratively and iterative convergences were investigated. Numerical coincidences with physical constants were explored.

Lambert W Function, Planck Radiation, Euler’s Equation, Transcendental Equation, Fine Structure Constant

Gnanarajan, S. (2021) Application of Lambert W Function to Planck Spectral Radiance Frequencies. Journal of Applied Mathematics and Physics, 9, 2500-2510. doi: 10.4236/jamp.2021.910160.