AppendixC 189(iii)thefirst correction to the zero temperature valueisproportionaltoT^2 .IfF(ε)is
areasonable power law ofε,then it will have a magnitude of order(kkkBT/μ)^2 times
thefirst term. Thefactor (π^2 / 6 ) which enters comes from the definite integral
∫∞0∫∫
y^2 exp(y)dy/[ 1 +exp(y)]^2 =π^2 / 6(whichis one ofthoseintegralsaphysicist maylookup, rather than prove?). The
expressionforμ(T)given at theendofsection 8.1.2isobtainedfrom equation (C.7)
usingF(ε)=
∫
0∫∫
∫ g(ε)dε. And equation (8.9) forU(T)is obtained withF(ε)=
0
∫∫
εg(ε)dε.