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Funcions, s铆mbols i car脿cters especials
| Tipus | Sintaxi | Com es veu |
| Accents i diacr铆tics |
acute{a} quad grave{a} quad breve{a} quad check{a} quad tilde{a} |
a 麓 a ` a 藰 a 藝 a ~ {displaystyle {acute {a}}quad {grave {a}}quad {breve {a}}quad {check {a}}quad {tilde {a}}}  |
| Funcions est脿ndard (b茅) |
sin x + ln y +operatorname{sgn} z text{ quan }x<y |
sin 鈦 x + ln 鈦 y + sgn 鈦 z 聽quan聽 x < y {displaystyle sin x+ln y+operatorname {sgn} z{text{ quan }}x<y}  |
| Funcions est脿ndard (malament) |
sin x + ln y + sgn z quan x<y |
s i n x + l n y + s g n z q u a n x < y {displaystyle sinx+lny+sgnzquanx<y,}  |
| Super铆ndexs i sub铆ndexs |
a^2 a_2 a^{2+1} a_{i,j} {}_1^2X_3^4 hat{a} bar{b} vec{c} overrightarrow{a b} overleftarrow{c d} widehat{d e f} overline{g h i} underline{j k l} |
a 2 聽 a 2 聽 a 2 + 1 聽 a i , j 聽 1 2 X 3 4 聽 聽 a ^ 聽 b 炉 聽 c 鈫 聽 a b 鈫 聽 c d 鈫 聽 d e f ^ 聽 g h i 炉 聽 j k l _ {displaystyle a^{2} a_{2} a^{2+1} a_{i,j} {}_{1}^{2}X_{3}^{4} {hat {a}} {bar {b}} {vec {c}} {overrightarrow {ab}} {overleftarrow {cd}} {widehat {def}} {overline {ghi}} {underline {jkl}}}  |
| M貌dul |
s_k equiv 0 pmod{m} |
s k 鈮 0 ( mod m ) {displaystyle s_{k}equiv 0{pmod {m}}}  |
| Derivades |
nabla partial x dx dot x ddot y a' a'' |
鈭 聽 鈭 x 聽 d x 聽 x 藱 聽 y 篓 聽 a 鈥 a 鈥 {displaystyle nabla partial x dx {dot {x}} {ddot {y}} a'a''}  |
| Sumatoris, l铆mits, integrals ... |
lim_{n to infty}x_n = int_{-n}^{n} e^x, dx = iint_{D} x, dx,dy |
lim n 鈫 鈭 x n = 鈭 鈭 n n e x d x = 鈭 D x d x d y {displaystyle lim _{nto infty }x_{n}=int _{-n}^{n}e^{x},dx=iint _{D}x,dx,dy}  |
| sum_{k=1}^n k^2 prod_{i=1}^n x_i coprod_{i=1}^n x_i bigcup_{iin N} A_i bigoplus_{j=1}^n B_j |
鈭 k = 1 n k 2 聽 鈭 i = 1 n x i 聽 鈭 i = 1 n x i 聽 鈰 i 鈭 N A i 聽 猕 j = 1 n B j {displaystyle sum _{k=1}^{n}k^{2} prod _{i=1}^{n}x_{i} coprod _{i=1}^{n}x_{i} bigcup _{iin mathbb {N} }A_{i} bigoplus _{j=1}^{n}B_{j}}  |
| Conjunts |
forall x notin varnothing subseteq A cap B cup exists {x,y} times C supsetneq B ni a |
鈭 x 鈭 鈭 鈯 A 鈭 B 鈭 鈭 { x , y } 脳 C 鈯 B 鈭 a {displaystyle forall xnot in varnothing subseteq Acap Bcup exists {x,y}times Csupsetneq Bni a}  |
| L貌gica |
p land bar{q} to plor lnot q |
p 鈭 q 炉 鈫 p 鈭 卢 q {displaystyle pland {bar {q}}to plor lnot q}  |
| Arrels |
sqrt{2}approx 1,4 le sqrt[n]{x} |
2 鈮 1 , 4 鈮 x n {displaystyle {sqrt {2}}approx 1,4leq {sqrt[{n}]{x}}} ![{displaystyle {sqrt {2}}approx 1,4leq {sqrt[{n}]{x}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/305b3ffdb5226a5125e9e39b5a28a2d8132170da) |
| Fraccions i matrius |
frac{2}{4}=0,5 {n choose k} |
2 4 = 0 , 5 聽 ( n k ) {displaystyle {frac {2}{4}}=0,5 {n choose k}}  |
| begin{matrix} x & y \ z & v end{matrix} begin{vmatrix} x & y \ z & v end{vmatrix} begin{pmatrix} x & y \ z & v end{pmatrix} |
x y z v 聽 | x y z v | 聽 ( x y z v ) {displaystyle {begin{matrix}x&y\z&vend{matrix}} {begin{vmatrix}x&y\z&vend{vmatrix}} {begin{pmatrix}x&y\z&vend{pmatrix}}}  |
| Relacions |
sim ; approx ; simeq ; cong ; le ; < ; ll ; gg ; ge ; > ; equiv ; notequiv ; ne ; propto ; pm ; mp |
鈭 鈮 鈮 鈮 鈮 < 鈮 鈮 鈮 > 鈮 鈮 鈮 鈭 卤 鈭 {displaystyle sim ;approx ;simeq ;cong ;leq ;<;ll ;gg ;geq ;>;equiv ;not equiv ;neq ;propto ;pm ;mp }  |
| Geometria |
alpha triangle angle perp | 45^circ |
伪 聽 鈻 聽 鈭 鈯 鈭 聽 45 鈭 {displaystyle alpha triangle angle perp | 45^{circ }}  |
| Fletxes |
leftarrow rightarrow leftrightarrow
longleftarrow longrightarrow
mapsto longmapsto
nearrow searrow swarrow nwarrow
uparrow downarrow updownarrow
|
鈫 聽 鈫 聽 鈫 {displaystyle leftarrow rightarrow leftrightarrow }  鉄 聽 鉄 {displaystyle longleftarrow longrightarrow }  鈫 聽 鉄 {displaystyle mapsto longmapsto }  鈫 聽 鈫 聽 鈫 聽 鈫 {displaystyle nearrow searrow swarrow nwarrow }  鈫 聽 鈫 聽 鈫 {displaystyle uparrow downarrow updownarrow } 
|
|
Leftarrow Rightarrow Leftrightarrow
Longleftarrow Longrightarrow Longleftrightarrow (o iff)
Uparrow Downarrow Updownarrow
|
鈬 聽 鈬 聽 鈬 {displaystyle Leftarrow Rightarrow Leftrightarrow }  鉄 聽 鉄 聽 鉄 {displaystyle Longleftarrow Longrightarrow iff }  鈬 聽 鈬 聽 鈬 {displaystyle Uparrow Downarrow Updownarrow } 
|
|
xrightarrow[text~opcional]{text} xleftarrow{text}
|
鈫 t e x t 聽 o p c i o n a l t e x t 鈫 t e x t {displaystyle {xrightarrow[{text~opcional}]{text}}{xleftarrow {text}}} ![{displaystyle {xrightarrow[{text~opcional}]{text}}{xleftarrow {text}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/5f9f5922135d984f711fde896f1f83ca3880bd20)
|
| Especial |
oplus otimes pm mp hbar wr dagger ddagger star * ldots circ cdot times bullet infty vdash models |
鈯 鈯 卤 鈭 鈩 鈮 鈥 鈥 鈰 鈭 鈥 {displaystyle oplus otimes pm mp hbar wr dagger ddagger star *ldots }  鈭 鈰 脳 鈭 聽 鈭 聽 鈯 聽 鈯 {displaystyle circ cdot times bullet infty vdash models }  |
| Extra: |
mathcal{A} mathcal{C} mathcal{H}... mathfrak{P} mathfrak{a} mathfrak{p}... N Z Q R C mathbb{P} |
A C H . . . 聽 P a p . . . 聽 N Z Q R C P {displaystyle {mathcal {A}}{mathcal {C}}{mathcal {H}}... {mathfrak {P}}{mathfrak {a}}{mathfrak {p}}... mathbb {N} mathbb {Z} mathbb {Q} mathbb {R} mathbb {C} mathbb {P} }  |
Per a la resta de funcions, vegeu m:Help:Formula
Exemples
F贸rmula de l'equaci贸 quadr脿tica
x
1
,
2
=
鈭
b
卤
b
2
鈭
4
a
c
2
a
{displaystyle x_{1,2}={frac {-bpm {sqrt {b^{2}-4ac}}}{2a}}}
<math>x_{1,2}=frac{-bpmsqrt{b^2-4ac}}{2a}</math>
Par猫ntesis i fraccions
2
=
(
(
3
鈭
x
)
鈰
2
3
鈭
x
)
{displaystyle 2=left({frac {left(3-xright)cdot 2}{3-x}}right)}
<math>2 = left( frac{left(3-xright) cdot 2}{3-x} right)</math>
Integrals
鈭
a
x
鈭
a
s
f
(
y
)
d
y
d
s
=
鈭
a
x
f
(
y
)
(
x
鈭
y
)
d
y
{displaystyle int _{a}^{x}int _{a}^{s}f(y),dy,ds=int _{a}^{x}f(y)(x-y),dy}
<math>int_a^x int_a^s f(y),dy,ds = int_a^x f(y)(x-y),dy</math>
Sumatoris
鈭
m
=
1
鈭
鈭
n
=
1
鈭
m
2
n
3
m
(
m
3
n
+
n
3
m
)
{displaystyle sum _{m=1}^{infty }sum _{n=1}^{infty }{frac {m^{2},n}{3^{m}left(m,3^{n}+n,3^{m}right)}}}
<math>sum_{m=1}^inftysum_{n=1}^inftyfrac{m^2,n}
{3^mleft(m,3^n+n,3^mright)}</math>
Equaci贸 Diferencial
u
鈥
+
p
(
x
)
u
鈥
+
q
(
x
)
u
=
f
(
x
)
,
x
>
a
{displaystyle u''+p(x)u'+q(x)u=f(x),quad x>a}
<math>u'' + p(x)u' + q(x)u=f(x),quad x>a</math>
Nombres Complexos
|
z
炉
|
=
|
z
|
,
聽
|
(
z
炉
)
n
|
=
|
z
|
n
,
arg
鈦
(
z
n
)
=
n
arg
鈦
(
z
)
{displaystyle |{bar {z}}|=|z|, |({bar {z}})^{n}|=|z|^{n},arg(z^{n})=narg(z),}
<math>|bar{z}| = |z|, |(bar{z})^n| = |z|^n, arg(z^n) = n arg(z),</math>
L铆mits
lim
z
鈫
z
0
f
(
z
)
=
f
(
z
0
)
{displaystyle lim _{zrightarrow z_{0}}f(z)=f(z_{0}),}
<math>lim_{zrightarrow z_0} f(z)=f(z_0),</math>
Integrals
蠒
n
(
魏
)
=
1
4
蟺
2
魏
2
鈭
0
鈭
sin
鈦
(
魏
R
)
魏
R
鈭
鈭
R
[
R
2
鈭
D
n
(
R
)
鈭
R
]
d
R
{displaystyle phi _{n}(kappa )={frac {1}{4pi ^{2}kappa ^{2}}}int _{0}^{infty }{frac {sin(kappa R)}{kappa R}}{frac {partial }{partial R}}left[R^{2}{frac {partial D_{n}(R)}{partial R}}right],dR}
![{displaystyle phi _{n}(kappa )={frac {1}{4pi ^{2}kappa ^{2}}}int _{0}^{infty }{frac {sin(kappa R)}{kappa R}}{frac {partial }{partial R}}left[R^{2}{frac {partial D_{n}(R)}{partial R}}right],dR}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7f6695154ee0e388c6ea1da20c2e19810282251a)
<math>phi_n(kappa) = frac{1}{4pi^2kappa^2} int_0^infty
frac{sin(kappa R)}{kappa R} frac{partial}{partial R}left[R^2frac{partial
D_n(R)}{partial R}right],dR</math>
Integrals
蠒
n
(
魏
)
=
0.033
C
n
2
魏
鈭
11
/
3
,
1
L
0
鈮
魏
鈮
1
l
0
{displaystyle phi _{n}(kappa )=0.033C_{n}^{2}kappa ^{-11/3},quad {frac {1}{L_{0}}}ll kappa ll {frac {1}{l_{0}}},}
<math>phi_n(kappa) =
0.033C_n^2kappa^{-11/3},quad frac{1}{L_0}llkappallfrac{1}{l_0},</math>
Claus i casos
f
(
x
)
=
{
1
鈭
1
鈮
x
<
0
1
2
x
=
0
x
0
<
x
鈮
1
{displaystyle f(x)={begin{cases}1&-1leq x<0\{frac {1}{2}}&x=0\x&0<xleq 1end{cases}}}
<math>f(x) = begin{cases}1 & -1 le x < 0\
frac{1}{2} & x = 0\x&0<xle 1end{cases}</math>
Sub铆ndexs
p
F
q
(
a
1
,
.
.
.
,
a
p
;
c
1
,
.
.
.
,
c
q
;
z
)
=
鈭
n
=
0
鈭
(
a
1
)
n
鈰
鈰
鈰
(
a
p
)
n
(
c
1
)
n
鈰
鈰
鈰
(
c
q
)
n
z
n
n
!
{displaystyle {}_{p}F_{q}(a_{1},...,a_{p};c_{1},...,c_{q};z)=sum _{n=0}^{infty }{frac {(a_{1})_{n}cdot cdot cdot (a_{p})_{n}}{(c_{1})_{n}cdot cdot cdot (c_{q})_{n}}}{frac {z^{n}}{n!}},}
<math>{}_pF_q(a_1,...,a_p;c_1,...,c_q;z) = sum_{n=0}^infty
frac{(a_1)_ncdotcdotcdot(a_p)_n}{(c_1)_ncdotcdotcdot(c_q)_n}frac{z^n}{n!},</math>
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