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$$\sum_{i=1}^n a_i=0$$
∑ i = 1 n a i = 0 \sum_{i=1}^n a_i=0 i=1∑nai=0
$$\begin{pmatrix}1 & x & x^2 & \cdots \\1 & y & y^2 \\1 & z & z^2 \\\end{pmatrix}
$$
( 1 x x 2 ⋯ 1 y y 2 1 z z 2 ) \begin{pmatrix} 1 & x & x^2 & \cdots \\ 1 & y & y^2 \\ 1 & z & z^2 \\ \end{pmatrix} ⎝⎛111xyzx2y2z2⋯⎠⎞
$$ \sum_{n=1}^\infty \frac{1}{n^2} \to \textstyle \sum_{n=1}^\infty \frac{1}{n^2} \to \displaystyle \sum_{n=1}^\infty \frac{1}{n^2}
$$
∑ n = 1 ∞ 1 n 2 → ∑ n = 1 ∞ 1 n 2 → ∑ n = 1 ∞ 1 n 2 \sum_{n=1}^\infty \frac{1}{n^2} \to \textstyle \sum_{n=1}^\infty \frac{1}{n^2} \to \displaystyle \sum_{n=1}^\infty \frac{1}{n^2} n=1∑∞n21→∑n=1∞n21→n=1∑∞n21
\varGamma(x)= \frac{\int_{\alpha}^{\beta}g(t)(x-t)^2\text{d}t}{\phi(x)\sum_{0}^{N-1} \omega_i} \tag{2}
(2) Γ ( x ) = ∫ α β g ( t ) ( x − t ) 2 d t ϕ ( x ) ∑ 0 N − 1 ω i \varGamma(x)= \frac{\int_{\alpha}^{\beta}g(t)(x-t)^2\text{d}t}{\phi(x)\sum_{0}^{N-1} \omega_i} \tag{2} Γ(x)=ϕ(x)∑0N−1ωi∫αβg(t)(x−t)2dt(2)
\lim_{x \to 0}\frac{3x^2+7x^3}{x^2+5x^4}
lim x → 0 3 x 2 + 7 x 3 x 2 + 5 x 4 \lim_{x \to 0}\frac{3x^2+7x^3}{x^2+5x^4} x→0limx2+5x43x2+7x3
\int_0^{+\infty}x^ne^{-x}\text{d}x=n!
∫ 0 + ∞ x n e − x d x = n ! \int_0^{+\infty}x^ne^{-x}\text{d}x=n! ∫0+∞xne−xdx=n!
\int_{x^2+y^2 \leq R^2}f(x,y)\text{d}x\text{d}y
∫ x 2 + y 2 ≤ R 2 f ( x , y ) d x d y \int_{x^2+y^2 \leq R^2}f(x,y)\text{d}x\text{d}y ∫x2+y2≤R2f(x,y)dxdy
\int_{x^2+y^2 \leq R^2}\!\!\!f(x,y)\text{d}x\text{d}y
∫ x 2 + y 2 ≤ R 2 ​​​ f ( x , y ) d x d y \int_{x^2+y^2 \leq R^2}\!\!\!f(x,y)\text{d}x\text{d}y ∫x2+y2≤R2f(x,y)dxdy
p(z^{(i)}=j | x^{(i)};\phi,\mu,\sum)=\frac{p(x^{(i)} | z^{(i)}=j; \mu)p(z^{(i)}=j;\phi)} {\sum_{l=1}^kp(x^{(i)}|z^{(i)}=l;\mu,\sum)p(z^{(i)}=j;\phi) } \tag{1}
(1) p ( z ( i ) = j ∣ x ( i ) ; ϕ , μ , ∑ ) = p ( x ( i ) ∣ z ( i ) = j ; μ ) p ( z ( i ) = j ; ϕ ) ∑ l = 1 k p ( x ( i ) ∣ z ( i ) = l ; μ , ∑ ) p ( z ( i ) = j ; ϕ ) p(z^{(i)}=j | x^{(i)};\phi,\mu,\sum)=\frac{p(x^{(i)} | z^{(i)}=j; \mu)p(z^{(i)}=j;\phi)} {\sum_{l=1}^kp(x^{(i)}|z^{(i)}=l;\mu,\sum)p(z^{(i)}=j;\phi) } \tag{1} p(z(i)=j∣x(i);ϕ,μ,∑)=∑l=1kp(x(i)∣z(i)=l;μ,∑)p(z(i)=j;ϕ)p(x(i)∣z(i)=j;μ)p(z(i)=j;ϕ)(1)
$$\begin{pmatrix}1 & a_1 & a_1^2 & \cdots & a_1^n \\1 & a_2 & a_2^2 & \cdots & a_2^n \\\vdots & \vdots & \vdots & \ddots & \vdots \\1 & a_m & a_m^2 & \cdots & a_m^n \\\end{pmatrix}$$
( 1 a 1 a 1 2 ⋯ a 1 n 1 a 2 a 2 2 ⋯ a 2 n ⋮ ⋮ ⋮ ⋱ ⋮ 1 a m a m 2 ⋯ a m n ) \begin{pmatrix} 1 & a_1 & a_1^2 & \cdots & a_1^n \\ 1 & a_2 & a_2^2 & \cdots & a_2^n \\ \vdots & \vdots & \vdots & \ddots & \vdots \\ 1 & a_m & a_m^2 & \cdots & a_m^n \\ \end{pmatrix} ⎝⎜⎜⎜⎛11⋮1a1a2⋮ama12a22⋮am2⋯⋯⋱⋯a1na2n⋮amn⎠⎟⎟⎟⎞
这些不需要记忆，类似于手册性质的要用即查
参考：
1.https://blog.csdn.net/yeler082/article/details/80718212
2.https://blog.csdn.net/qq_40587575/article/details/83387333
3.https://math.meta.stackexchange.com/questions/5020/mathjax-basic-tutorial-and-quick-reference?newreg=f0af40c6705a43bf9002835c94bc3c78
4.https://www.cnblogs.com/JohnTsai/p/4027229.html
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