## Analytical foundations of physical statistics |

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anti-symmetric approximate aras assume asymptotic expression asymptotic formulae Bose-Einstein statistics calculations central limit theorem characteristic value classical mechanics complete orthogonal system definition of measure depends distributed according distribution law energy levels energy operator equal equation evaluation fc=l Fermi-Dirac statistics formula 23 formula 38 function F Gibbs given system gives Hamiltonian variables i-th particle index of symmetry infinite series integral large number last sum law pk mathematical expectation Maxwell-Boltzmann statistics mean F microcanonical mean mutually independent random number of fundamental number of particles number of solutions obtained obviously occupation numbers parameters phase function photons probability theory quantum physics r=l r=l random quantities right hand side sake of brevity sequel Statistical Mechanics statistical physics statistical schemes statistical theory statistics The formula structure function summation is extended summatory quantities symmetric characteristic functions symmetric statistics system G2 thermostat three statistics tion volume occupied