latex 常用数学符号(数值函数、根式、微分与导数、模运算、极限、范围与预测)

目录

  • 数值函数
  • 根式
  • 微分与导数
  • 模运算
  • 极限
  • 范围与预测

数值函数

符号 latex
exp ⁡ a b = a b \exp_a b = a^b expab=ab \exp_a b = a^b
exp ⁡ b = e b \exp b = e^b expb=eb \exp b = e^b
1 0 m 10^m 10m 10^m
ln ⁡ c \ln c lnc \ln c
lg ⁡ d = log ⁡ e \lg d = \log e lgd=loge \lg d = \log e
log ⁡ 10 f \log_{10} f log10f \log_{10} f
sin ⁡ a \sin a sina \sin a
cos ⁡ b \cos b cosb \cos b
tan ⁡ c \tan c tanc \tan c
cot ⁡ d \cot d cotd \cot d
sec ⁡ e \sec e sece \sec e
csc ⁡ f \csc f cscf \csc f
arcsin ⁡ a \arcsin a arcsina \arcsin a
arccos ⁡ b \arccos b arccosb \arccos b
arctan ⁡ c \arctan c arctanc \arctan c
arccot ⁡ d \operatorname{arccot} d arccotd \operatorname{arccot} d
arcsec ⁡ d \operatorname{arcsec} d arcsecd \operatorname{arcsec} d
arccsc ⁡ d \operatorname{arccsc} d arccscd \operatorname{arccsc} d
sinh ⁡ a \sinh a sinha \sinh a
cosh ⁡ a \cosh a cosha \cosh a
tanh ⁡ a \tanh a tanha \tanh a
coth ⁡ a \coth a cotha \coth a
sh ⁡ d \operatorname{sh} d shd \operatorname{sh} d
ch ⁡ d \operatorname{ch} d chd \operatorname{ch} d
th ⁡ d \operatorname{th} d thd \operatorname{th} d
coth ⁡ d \operatorname{coth} d cothd \operatorname{coth} d
argsh ⁡ d \operatorname{argsh} d argshd \operatorname{argsh} d
argch ⁡ d \operatorname{argch} d argchd \operatorname{argch} d
argth ⁡ d \operatorname{argth} d argthd \operatorname{argth} d
sgn ⁡ d \operatorname{sgn} d sgnd \operatorname{sgn} d
∣ s ∣ \left\vert s \right\vert s \left\vert s \right\vert
min ⁡ ( x , y ) \min(x,y) min(x,y) \min(x,y)
max ⁡ ( x , y ) \max(x,y) max(x,y) \max(x,y)

根式

符号 latex
√ \surd \surd
3 \sqrt{3} 3 \sqrt{3}
3 n \sqrt[n]{3} n3 \sqrt[n]{3}
x 3 + y 3 2 3 \sqrt[3]{\frac{x^3+y^3}{2}} 32x3+y3 \sqrt[3]{\frac{x^3+y^3}{2}}

微分与导数

符号 latex
d t dt dt dt
d t \mathrm{d}t dt \mathrm{d}t
∂ t \partial t t \partial t
∇ ψ \nabla\psi ψ \nabla\psi
d y / d x , d y / d x dy/dx, \mathrm{d}y/\mathrm{d}x dy/dx,dy/dx dy/dx, \mathrm{d}y/\mathrm{d}x
d y d x , d y d x \frac{dy}{dx}, \frac{\mathrm{d}y}{\mathrm{d}x} dxdy,dxdy \frac{dy}{dx}, \frac{\mathrm{d}y}{\mathrm{d}x}
∂ 2 ∂ x 1 ∂ x 2 y \frac{\partial^2}{\partial x_1\partial x_2}y x1x22y \frac{\partial^2}{\partial x_1\partial x_2}y
′ , ‵ \prime, \backprime , \prime, \backprime
f ′ , f ′ , f ′ ′ , f ( 3 ) f^\prime, f', f'', f^{(3)} f,f,f′′,f(3) f^\prime, f’, f’', f^{(3)}
y ˙ , y ¨ \dot y, \ddot y y˙,y¨ \dot y, \ddot y

模运算

符号 latex
s k ≡ 0 ( m o d m ) s_k \equiv 0 \pmod{m} sk0(modm) s_k \equiv 0 \pmod{m}
a   m o d   b a \bmod b amodb a \bmod b
gcd ⁡ ( m , n ) \gcd(m, n) gcd(m,n) \gcd(m, n)
lcm ⁡ ( m , n ) \operatorname{lcm}(m, n) lcm(m,n) \operatorname{lcm}(m, n)
∣ , ∤ , ∣ , ∤ \mid, \nmid, \shortmid, \nshortmid ,,, \mid, \nmid, \shortmid, \nshortmid

极限

符号 latex
lim ⁡ n → ∞ x n \lim_{n \to \infty}x_n limnxn \lim_{n \to \infty}x_n
lim ⁡ n → ∞ x n \textstyle \lim_{n \to \infty}x_n limnxn \textstyle \lim_{n \to \infty}x_n

范围与预测

符号 latex
min ⁡ x , max ⁡ y , inf ⁡ s , sup ⁡ t \min x, \max y, \inf s, \sup t minx,maxy,infs,supt \min x, \max y, \inf s, \sup t
lim ⁡ u , lim inf ⁡ v , lim sup ⁡ w \lim u, \liminf v, \limsup w limu,liminfv,limsupw \lim u, \liminf v, \limsup w
dim ⁡ p , deg ⁡ q , det ⁡ m , ker ⁡ ϕ \dim p, \deg q, \det m, \ker\phi dimp,degq,detm,kerϕ \dim p, \deg q, \det m, \ker\phi
Pr ⁡ j , hom ⁡ l , ∥ z ∥ , arg ⁡ z \Pr j, \hom l, \lVert z \rVert, \arg z Prj,homl,z,argz \Pr j, \hom l, \lVert z \rVert, \arg z

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