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ζ
k
(a)
a f(n, T ) a
ζ
3/2
(a)
ζ
3/2
(a)
f
max
a
a = 1 ζ
3/2
f
max
= ζ
3/2
≈ 2.6
µ
a → 1 n
0
T
0
f
max
= n
0
(kT
0
)
−3/2
/A
α
= µ = 0 T = T
0
n
0
T
0
n
0
T
0
n = n
0
+ δn T = T
0
+ δT δn δT
f(µ, T ) =
n
0
A(kT
0
)
3/2
+
δn
A(kT
0
)
3/2
−
3
2
n
0
A(kT
0
)
3/2
δT
T
0
.
µ = 0 n = n
0
T = T
0
ζ
3/2
(e
µ/(kT )
) =
1
Γ(3/2)
Z
∞
0
dxx
1/2
e
x−µ/(kT )
− 1
µ → 0 T → T
0
µ = 0 f
max
δn − 3n
0
δT/(2T
0
)
A(kT
0
)
3/2
=
1
Γ(3/2)
Z
∞
0
dxx
1/2
(e
x
− e
x−µ/(kT )
)
(e
x−µ/(kT )
− 1)(e
x
− 1)
.
