TITLE:
Application of Lambert W Function to Planck Spectral Radiance Frequencies
AUTHORS:
Sabaratnasingam Gnanarajan
KEYWORDS:
Lambert W Function, Planck Radiation, Euler’s Equation, Transcendental Equation, Fine Structure Constant
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.9 No.10,
October
27,
2021
ABSTRACT: 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.