A semi-analytical approach to black body radiation

TL;DR

This paper introduces a semi-analytical method leveraging polylogarithm functions to calculate black body radiation between two frequencies, and applies it to estimate solar radiation received at Earth's surface.

Contribution

The paper presents a novel semi-analytical approach for black body radiation calculations that simplifies the process using polylogarithm functions.

Findings

Efficient calculation of black body radiance between two frequencies.

Application to estimate solar radiation at Earth's surface.

Validation of the method against known models.

Abstract

We describe a semi-analytical method to calculate the total radiance received form a black body, between two frequencies. As has been done before, the method takes advantage of the fact that the solution simplifies with the use of polylogarithm functions. We then use it to study the amount of radiation from the sun received by bodies at Earths surface.