LaTeX Math rendering

Rendering math equations in LaTeX style.

Change the Hexo markdown renderer

This guide is partly from the Hexo Next docs for math equations

Uninstall the default Markdown renderer (hexo-renderer-marked) because it confuses \ and _ character in the math equations as Markdown syntax.

npm un hexo-renderer-marked

Then you can choose between the pandoc (with MathJax) or the markdown-it (with KaTeX) renderer.

• pandoc + MathJax
• markdown-it

Pandoc and MathJax

Install pandoc and the Hexo renderer.

npm i hexo-renderer-pandoc

And activate MathJax in the theme config.

_config.next.yml

math:
  every_page: false
  mathjax:
    enable: true
    # Available values: none | ams | all
    tags: none

Set mathjax: true in the page frontmatter to load the MathJax library.

You can also install hexo-filter-mathjax for rendering math equations server-side.

Katex

⚠️ Chemical expressions are not supported in this setup.

1. Install the markdown-it renderer and KaTeX plugin.

npm i hexo-renderer-markdown-it @iktakahiro/markdown-it-katex

2. Add KaTeX to markdown-it's plugin list:

_config.yml

markdown:
  plugins:
    - "@iktakahiro/markdown-it-katex"
    - (Other plugins ...)

3. enable KaTeX in the theme config.

_config.next.yml

math:
  every_page: false
  mathjax:
    enable: true
    # Available values: none | ams | all
    tags: none

Set mathjax: true (yesp, not katex) in the frontmatter to load the math library.

MathJax (Server-side rendering alternative)

Install markdown-it-latex2img to convert math expressions to SVG images online with MathJax at https://math.now.sh/.

⚠️ However, it does not play well with dark mode. The text will still be black and invisible. And it may mess with fancybox image gallery.

npm i hexo-renderer-markdown-it markdown-it-latex2img

_config.yml

markdown:
  plugins:
    - markdown-it-latex2img
    - (other plugins...)

Math rendering Guide

For examples, see MathJax quick reference and KaTeX performance test.

Inline math examples

Enclosed by $...$

• Pythagoras theorem: $a^2+b^2=c^2$
• Sum of arithmetic sequence: $S_{n}=n a_{1}+\frac{n(n-1)}{2} d, n \in N^{*}$
• Fundamental theorem of calculus: $\int_{a}^{b} f(x) d x=F(b)-F(a)=\left.F(x)\right|_{a} ^{b}$
• Binomial distribution: $P_{n}(k)=C_{n}^{k} p^{k} q^{n-k} \quad k=0,1,2 \ldots \ldots, n$
• Greek letters: $\Gamma\ \Delta\ \Theta\ \Lambda\ \Xi\ \Pi\ \Sigma\ \Upsilon\ \Phi\ \Psi\ \Omega$

Block math examples

Enclosed by $$...$$

Repeating fractions

$$ \frac{1}{\Bigl(\sqrt{\phi \sqrt{5}}-\phi\Bigr) e^{\frac25 \pi}} \equiv 1+\frac{e^{-2\pi}} {1+\frac{e^{-4\pi}} {1+\frac{e^{-6\pi}} {1+\frac{e^{-8\pi}} {1+\cdots} } } } $$

Summation notation

$$ \left( \sum_{k=1}^n a_k b_k \right)^2 \leq \left( \sum_{k=1}^n a_k^2 \right) \left( \sum_{k=1}^n b_k^2 \right) $$

Probability density of normal distribution

$$ f(x) = \frac{1}{\sqrt{2\pi}\sigma}e^{-\frac{(x-\mu)^2}{2\sigma^2}} $$

The ratio of two consecutive numbers in Fibonacci Sequence

$$\lim_{n\to \infty}\frac{A_{n-1}}{A_n}=\frac{\sqrt{5}-1}{2}.$$

Factorisation

$$ \begin{aligned}(x−1)(x−3)&=x^2−4x+3 \cr &=x^2−4x+4−1 \cr &=(x−2)^2−1 \end{aligned} $$

Dirichlet function

$$ D(x)= \begin{cases} 1,& x \in Q \cr 0,& x \notin Q \end{cases} $$

Gauss's law

$$ \iiint_{\Omega}\left(\frac{\partial P}{\partial x}+\frac{\partial Q}{\partial y}+\frac{\partial R}{\partial z}\right) d v=\iint_{\Sigma} P d y d z+Q d z d x+R d x d y $$

Vandermonde matrix

$$D_{n-1}=\left|\begin{array}{cccc} 1 & 1 & \dots & 1 \cr x_{2} & x_{3} & \dots & x_{n} \cr \vdots & \vdots & & \vdots \cr x_{2}^{n-2} & x_{3}^{n-2} & \dots & x_{n}^{n-2} \end{array}\right|=\prod_{2 \leq j<i \leq n}\left(x_{i}-x_{j}\right)$$

System of linear equations

$$ \left\lbrace \begin{aligned} a_{11} x_{1}+a_{12} x_{2}+\cdots+a_{1 n} x_{n} &=b_{1} \cr a_{21} x_{1}+a_{22} x_{2}+\cdots+a_{2 n} x_{n} &=b_{2} \cr \cdots \cdots \cdots \cr a_{m 1} x_{1}+a_{m 2} x_{2}+\cdots+a_{m n} x_{n} &=b_{m} \end{aligned} \right\rbrace $$

Lorenz Equations

$$ \begin{aligned} \dot{x} &= \sigma(y-x) \cr \dot{y} &= \rho x - y - xz \cr \dot{z} &= -\beta z + xy \end{aligned} $$

Cross Product

$$ \mathbf{V}_1 \times \mathbf{V}_2 = \begin{vmatrix} \mathbf{i} &\mathbf{j} &\mathbf{k} \cr \frac{\partial X}{\partial u} & \frac{\partial Y}{\partial u} &0 \cr \frac{\partial X}{\partial v} & \frac{\partial Y}{\partial v} &0 \end{vmatrix} $$

Maxwell's Equations

$$ \begin{aligned} \nabla \times \vec{\mathbf{B}} -, \frac1c, \frac{\partial\vec{\mathbf{E}}}{\partial t} &= \frac{4\pi}{c}\vec{\mathbf{j}} \cr \nabla \cdot \vec{\mathbf{E}} &= 4 \pi \rho \cr \nabla \times \vec{\mathbf{E}}, +, \frac1c, \frac{\partial\vec{\mathbf{B}}}{\partial t} &= \vec{\mathbf{0}} \cr \nabla \cdot \vec{\mathbf{B}} &= 0 \end{aligned} $$