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Bose-Einstein Distribution

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A distribution which arises in the study of integer spin particles in physics,

P(k)=(k^s)/(e^(k-mu)-1).
(1)

Its integral is given by

int_0^infty(k^sdk)/(e^(k-mu)-1)=e^muGamma(s+1)Phi(e^mu,s+1,1)
(2)
=Gamma(s+1)Li_(1+s)(e^mu)
(3)

for R[s]>-1, where Phi(z,s,a) is the Lerch transcendent and Li_n(z) is a polylogarithm.

See also

Einstein Functions, Fermi-Dirac Distribution, Sigmoid Function

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Cite this as:

Weisstein, Eric W. "Bose-Einstein Distribution." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Bose-EinsteinDistribution.html

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