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has been cited by the following article:

• TITLE: New Probability Distributions in Astrophysics: IV. The Relativistic Maxwell-Boltzmann Distribution

  AUTHORS: Lorenzo Zaninetti

  KEYWORDS: 05.20.-y Classical Statistical Mechanics, 05.20.Dd Kinetic Theory

  JOURNAL NAME: International Journal of Astronomy and Astrophysics, Vol.10 No.4, December 10, 2020

  ABSTRACT: Two relativistic distributions which generalize the Maxwell Boltzman (MB) distribution are analyzed: the relativistic MB and the Maxwell-Jüttner (MJ) distribution. For the two distributions, we derived in terms of special functions the constant of normalization, the average value, the second moment about the origin, the variance, the mode, the asymptotic behavior, approximate expressions for the average value as function of the temperature and the connected inverted expressions for the temperature as function of the average value. Two astrophysical applications to the synchrotron emission in presence of the magnetic field and the relativistic electrons are presented.