1
Long Equations
Here is a long equation without line number.
Z
Z
Θ(fε (t)) dµ(t) = −
fε4 (t) dµ(t)
G
G
Z
Z
2
2
2
2
+ (b + 2a )
fε (t) dµ(t) + a2 b2 − a4 .
fε (t) dµ(t) + 2ab
G
G
Here is the same long equation with a single equation number. The ”notag”
is used to suppress numbering the first line.
Z
Z
Θ(fε (t)) dµ(t) = −
fε4 (t) dµ(t)
G
G
Z
Z
+ (b2 + 2a2 )
fε2 (t) dµ(t) + 2ab2
fε (t) dµ(t) + a2 b2 − a4 . (1)
G
G
Here is the same long equation with a single equation number, but centered.
Here the combination of ”equation” and ”split” environments is used. We prefer
this version for numbered long equations.
Z
Z
Θ(fε (t)) dµ(t) = −
fε4 (t) dµ(t)
G
G
Z
Z
(2)
2
2
2
2
+ (b + 2a )
fε (t) dµ(t) + 2ab
fε (t) dµ(t) + a2 b2 − a4 .
G
2
G
Multiline Equations
Example 1.
Here is a string of equations typeset with gather.
Z π
Z π
1
1
an =
f (x)e−inx dx =
f0 (x)e−inx dx
2π −π
2π −π
Z π
Z π
Z ∞
1
1
e−inx
−inx
= lim
fδn (x)e
dx = lim
gδn (t)
dx dt
1−α
n→∞ 2π −π
n→∞ 2π −∞
−π |x − t|
Z π
1
=
U µ (x)e−inx dx.
2π −π α
Here is the same set of equations typeset with align.
Z π
Z π
1
1
an =
f (x)e−inx dx =
f0 (x)e−inx dx
2π −π
2π −π
Z π
Z π
Z ∞
1
1
e−inx
= lim
fδn (x)e−inx dx = lim
gδn (t)
dx
dt
1−α
n→∞ 2π −π
n→∞ 2π −∞
−π |x − t|
Z π
1
=
U µ (x)e−inx dx.
2π −π α
1
Each of these two versions has advantages over the other. The first looks
better on the page while the second highlights the fact that a formula for
an is underway.
The second formulation introduces an ”overfill” on the second line, however, so must be altered to fit on the page properly. Here is a reformulation.
Z π
Z π
1
1
f (x)e−inx dx =
f0 (x)e−inx dx
an =
2π −π
2π −π
Z π
1
= lim
fδn (x)e−inx dx
n→∞ 2π −π
Z π
Z ∞
1
e−inx
= lim
gδn (t)
dx
dt
1−α
n→∞ 2π −∞
−π |x − t|
Z π
1
=
U µ (x)e−inx dx.
2π −π α
We prefer this third version.
Example 2.
Here is a common alignment first without line number, then with.
X
qj N
0
P (GN ) ≤
P kBj kT >
4 T
µ
2
≤
<j≤µ
X
µ
2 <j≤µ
4T 0
3/2
C qj (log pj+1 )
N qj T
4T 0
3/2
C µ (log pµ+1 )
N T
4T CT0
3(µ + 1)l
≤
µ exp
,
N
γ
≤
P (GN ) ≤
X
P
µ
2 <j≤µ
≤
X
µ
2 <j≤µ
kBj0 kT
qj N
>
4 T
4T 0
3/2
C qj (log pj+1 )
N qj T
4T 0
3/2
C µ (log pµ+1 )
N T
4T CT0
3(µ + 1)l
≤
µ exp
,
N
γ
≤
2
(3)
Here is one more example of a numbered multiline equation.
1
e−s
e−(hk −1)s
e−(hk +1)s
e−2hk s
+
+ ··· +
−
− ··· −
hk
hk − 1
1
1
hk
hX
hX
k −1
k −1
−js
−(2hk −j)s
e
e
=
−
(4)
hk − j
hk − j
j=0
j=0
Pk (s) =
=
hk
X
e−(hk −n)s − e−(hk +n)s
.
n
n=1
3