ds
146.6.203.178 (talk ) 12:59, 31 March 2009 (UTC)
chris: this thing
∯
integral limit tests
j
^
∂
β
Ω
χ
{\displaystyle {\hat {j}}\partial \beta \Omega \chi }
j
^
∂
β
θ
χ
{\displaystyle {\hat {j}}\partial \beta \theta \chi }
∫
a
b
f
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x
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d
x
=
F
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x
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|
x
=
a
x
=
b
{\displaystyle \int _{a}^{b}f(x)dx=F(x)|_{x=a}^{x=b}}
∫
a
b
f
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x
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d
x
=
F
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x
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|
x
=
a
x
=
b
{\displaystyle \int _{a}^{b}f(x)dx=F(x)|_{x=a}^{x=b}}
Failed to parse (unknown function "\cursive"): {\displaystyle \cursive{EBHM}}
images interfering with code
image overlap test
int main ()
int main ()
int main ()
int main ()
int main ()
int main ()
int main ()
int main ()
int main ()
int main ()
int main ()
int main ()
int main ()
int main ()
reference pages
editing math formulas
adding images
mathml chars
math toys
watchlist
Benford's Law
latex test
ϕ
(
t
)
=
∠
x
a
(
t
)
{\displaystyle \phi (t)=\angle {x_{a}(t)}}
I
R
−
G
=
q
A
n
i
2
τ
0
W
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e
q
V
A
/
k
T
)
(
1
+
V
b
i
−
V
A
k
T
/
q
τ
n
τ
p
2
τ
0
e
q
V
A
/
2
k
T
)
{\displaystyle I_{R-G}={{qAn_{i} \over 2\tau _{0}}W}{(e^{qV_{A}/kT}) \over ({1+{{V_{bi}-V_{A}} \over {kT/q}}{{\sqrt {\tau _{n}\tau _{p}}} \over 2\tau _{0}}{e^{qV_{A}/2kT}}})}}
e
i
π
+
1
=
0
{\displaystyle e^{i\pi }+1=0\,}
S
=
∑
m
=
1
∞
∑
n
=
1
∞
m
n
2
2
n
(
n
2
m
+
m
2
n
)
{\displaystyle S=\sum _{m=1}^{\infty }{\sum _{n=1}^{\infty }{mn^{2} \over 2^{n}(n2^{m}+m2^{n})}}}
S
=
1
2
(
∑
m
=
1
∞
∑
n
=
1
∞
m
n
2
2
n
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n
2
m
+
m
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n
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+
∑
m
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1
∞
∑
n
=
1
∞
m
n
2
2
n
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n
2
m
+
m
2
n
)
)
{\displaystyle S={1 \over 2}\left(\sum _{m=1}^{\infty }{\sum _{n=1}^{\infty }{mn^{2} \over 2^{n}(n2^{m}+m2^{n})}}+\sum _{m=1}^{\infty }{\sum _{n=1}^{\infty }{mn^{2} \over 2^{n}(n2^{m}+m2^{n})}}\right)}
S
=
1
2
(
∑
m
=
1
∞
∑
n
=
1
∞
m
2
n
2
m
(
n
2
m
+
m
2
n
)
+
∑
m
=
1
∞
∑
n
=
1
∞
m
n
2
2
n
(
n
2
m
+
m
2
n
)
)
{\displaystyle S={1 \over 2}\left(\sum _{m=1}^{\infty }{\sum _{n=1}^{\infty }{m^{2}n \over 2^{m}(n2^{m}+m2^{n})}}+\sum _{m=1}^{\infty }{\sum _{n=1}^{\infty }{mn^{2} \over 2^{n}(n2^{m}+m2^{n})}}\right)}
S
=
1
2
∑
m
=
1
∞
∑
n
=
1
∞
m
2
n
2
m
(
n
2
m
+
m
2
n
)
+
m
n
2
2
n
(
n
2
m
+
m
2
n
)
{\displaystyle S={1 \over 2}\sum _{m=1}^{\infty }{\sum _{n=1}^{\infty }{{m^{2}n \over 2^{m}(n2^{m}+m2^{n})}+{mn^{2} \over 2^{n}(n2^{m}+m2^{n})}}}}
S
=
1
2
∑
m
=
1
∞
∑
n
=
1
∞
m
2
n
2
n
+
n
2
m
2
m
2
m
2
n
(
n
2
m
+
m
2
n
)
{\displaystyle S={1 \over 2}\sum _{m=1}^{\infty }{\sum _{n=1}^{\infty }{m^{2}n2^{n}+n^{2}m2^{m} \over 2^{m}2^{n}(n2^{m}+m2^{n})}}}
S
=
1
2
∑
m
=
1
∞
∑
n
=
1
∞
m
n
2
m
2
n
=
1
2
(
∑
m
=
1
∞
m
2
m
)
2
{\displaystyle S={1 \over 2}\sum _{m=1}^{\infty }{\sum _{n=1}^{\infty }{mn \over 2^{m}2^{n}}}={1 \over 2}\left(\sum _{m=1}^{\infty }{m \over 2^{m}}\right)^{2}}
∑
m
=
1
∞
m
2
m
=
2
{\displaystyle \sum _{m=1}^{\infty }{m \over 2^{m}}=2}
S
=
2
{\displaystyle {S=2}}
y
(
t
)
=
cos
(
2
π
(
f
0
t
+
β
2
t
2
+
ϕ
0
)
)
{\displaystyle \displaystyle y(t)=\cos(2\pi (f_{0}t+{\beta \over 2}t^{2}+\phi _{0}))}
P
N
Z
Q
A
R
C
H
O
{\displaystyle \mathbb {PNZQARCHO} \ }
∑
x
=
0
100
f
(
x
)
{\displaystyle \sum _{x=0}^{100}f(x)}
...
d
f
(
t
)
d
x
{\displaystyle {\frac {df(t)}{dx}}}
...
x
2
3
{\displaystyle x^{2_{3}}}
...
∮
T
i
(
n
)
a
d
n
{\displaystyle \oint T_{i}(n)a\,dn}
...
∫
T
i
(
n
)
a
d
n
{\displaystyle \int T_{i}(n)a\,dn\,}
...
∫0 f (x ) dx ...
∑
t
=
i
N
(
a
)
{\displaystyle \sum _{t=i}N(a)\,}
...
a
x
2
+
b
x
+
c
=
0
{\displaystyle ax^{2}+bx+c=0}
...
a
x
2
+
b
x
+
c
=
0
{\displaystyle ax^{2}+bx+c=0\,}
∫
a
b
f
(
x
)
d
x
=
F
(
x
)
|
x
=
a
x
=
b
{\displaystyle \int _{a}^{b}f(x)dx=F(x)|_{x=a}^{x=b}}
bb:
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
{\displaystyle \mathbb {ABCDEFGHIJKLMNOPQRSTUVWXYZ} }
frak:
1234567890
a
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i
j
k
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m
n
o
p
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x
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z
A
B
C
D
E
F
G
H
I
J
K
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M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
{\displaystyle {\mathfrak {1234567890abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ}}}
cal:
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
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X
Y
Z
{\displaystyle {\mathcal {ABCDEFGHIJKLMNOPQRSTUVWXYZ}}}
bb:
1234567890
a
b
c
d
e
f
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h
i
j
k
l
m
n
o
p
q
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x
y
z
{\displaystyle \mathbb {1234567890abcdefghijklmnopqrstuvwxyz} }
cal:
1234567890
a
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j
k
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m
n
o
p
q
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s
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x
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z
{\displaystyle {\mathcal {1234567890abcdefghijklmnopqrstuvwxyz}}}
symb:
∫
∐
{\displaystyle \int \coprod }
∫
{\displaystyle {\begin{matrix}\int \end{matrix}}}
∐
{\displaystyle {\begin{matrix}\coprod \end{matrix}}}
cal not in symb:
45
a
p
q
s
x
{\displaystyle {\mathcal {45apqsx}}}
45
{\displaystyle {\mathcal {45}}}
, \mathcal{45} should be \bigtriangleup and \bigtriangledown
\mathcal{6} puts a slash through the next character
\mathcal{7} puts something through the next character
a
{\displaystyle {\mathcal {a}}}
, \mathcal{a} should be \dashv
\mathcal{p} puts a surd below the textline, should be \surd
\mathcal{x} = §
Latex symbols with no mirror counterparts: \Lleftarrow \multimap \rightsquigarrow
hierarchies
subsection
test test test
hyposubsection
test test test
this is a long line this is a long line this is a long line this is a long line this is a long line this is a long line this is a long line this is a long line this is a long line this is a long line this is a long line this is a long line this is a long line this is a long line this is a long line this is a long line this is a long line this is a long line this is a long line this is a long line
this is a long line this is a long line this is a long line this is a long line this is a long line this is a long line this is a long line this is a long line this is a long line this is a long line this is a long line this is a long line this is a long line this is a long line this is a long line this is a long line this is a long line this is a long line this is a long line this is a long line