TITLE:
Transport in Astrophysics: X. The Integral of the Planck Distribution
AUTHORS:
Lorenzo Zaninetti
KEYWORDS:
Stars: Atmospheres, Radiation Mechanisms: General, Blackbody Radiation
JOURNAL NAME:
International Journal of Astronomy and Astrophysics,
Vol.16 No.3,
September
1,
2026
ABSTRACT: The integral of the Planck distribution for radiation in the wavelength version can be integrated in terms of polylogarithms. We can therefore introduce a theoretical color theory for astronomical purposes. In particular, we investigate the two colors (B-V) and (U-B) and the bolometric correction in the framework of the incomplete Planck integral. Some of the astronomical variables of the Hertzsprung-Russel diagram, such as the absolute visual magnitude, radius, and mass, are derived as functions of (B-V) for nearby main sequence stars. The logarithm of the gravity is derived as a function of the temperature.