The CDF for the Boltzmann distribution
maybe approximated by means of the new special function [T.sub.[kappa],[mu]](x) as follows:
While LTE is established within the plasma, the population at different levels is governed by the Boltzmann distribution
While the intensity, depending on Boltzmann distribution
if the plasma at local thermal equilibrium, can be described as 
where [alpha], [beta] = x, y, z are tensor index, [OMEGA] is the volume of the unit cell, [f.sub.0] is the Boltzmann distribution
function, and [[sigma].sub.[alpha][beta]](e) is defined as
[C.sub.c] for the Boltzmann Distribution
in One Dimension.
The author has organized the main body of his text in seven chapters and six appendices devoted to energy and entropy, entropy and free energy, the evaporation of a liquid drop, gases and the basics of thermodynamics, mixtures and reactions, phases and temperature variations, heat dispersion and temperature, the Boltzmann distribution
law, and a wide variety of other related subjects.
To further illustrate the described procedures, [N.sub.2] in an equilibrium Boltzmann distribution
was chosen as a test case because its potential energy function is well known from high-resolution spectroscopic measurements.
Further approximations applied throughout this work are the assumption of a Boltzmann distribution
of the excited level population and the ideal gas law.
introduced a fractional Fokker-Planck equation (FFPE) which was shown to obey generalized Einstein relations, and its stationary solution is the Boltzmann distribution
A special way of assigning probabilities to values is the Boltzmann distribution
proposed by Sutton, defined as
The above distribution is called the Boltzmann distribution
(or Gibbs distribution), and was introduced in the context of the random generation of combinatorial objects by Douchon, Flajolet, Louchard and Schaeffer in 2004, see (4).