50 lines
1.3 KiB
Markdown
50 lines
1.3 KiB
Markdown
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---
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title: Math Sample
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subtitle: Using KaTeX
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date: 2017-03-05
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tags: ["example", "math"]
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---
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KaTeX can be used to generate complex math formulas server-side.
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$$
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\phi = \frac{(1+\sqrt{5})}{2} = 1.6180339887\cdots
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$$
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Additional details can be found on [GitHub](https://github.com/Khan/KaTeX) or on the [Wiki](http://tiddlywiki.com/plugins/tiddlywiki/katex/).
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<!--more-->
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### Example 1
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If the text between $$ contains newlines it will rendered in display mode:
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```
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$$
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f(x) = \int_{-\infty}^\infty\hat f(\xi)\,e^{2 \pi i \xi x}\,d\xi
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$$
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```
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$$
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f(x) = \int_{-\infty}^\infty\hat f(\xi)\,e^{2 \pi i \xi x}\,d\xi
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$$
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### Example 2
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```
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$$
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\frac{1}{\Bigl(\sqrt{\phi \sqrt{5}}-\phi\Bigr) e^{\frac25 \pi}} = 1+\frac{e^{-2\pi}} {1+\frac{e^{-4\pi}} {1+\frac{e^{-6\pi}} {1+\frac{e^{-8\pi}} {1+\cdots} } } }
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$$
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```
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$$
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\frac{1}{\Bigl(\sqrt{\phi \sqrt{5}}-\phi\Bigr) e^{\frac25 \pi}} = 1+\frac{e^{-2\pi}} {1+\frac{e^{-4\pi}} {1+\frac{e^{-6\pi}} {1+\frac{e^{-8\pi}} {1+\cdots} } } }
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$$
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### Example 3
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```
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$$
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1 + \frac{q^2}{(1-q)}+\frac{q^6}{(1-q)(1-q^2)}+\cdots = \prod_{j=0}^{\infty}\frac{1}{(1-q^{5j+2})(1-q^{5j+3})}, \quad\quad \text{for }\lvert q\rvert<1.
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$$
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```
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$$
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1 + \frac{q^2}{(1-q)}+\frac{q^6}{(1-q)(1-q^2)}+\cdots = \prod_{j=0}^{\infty}\frac{1}{(1-q^{5j+2})(1-q^{5j+3})}, \quad\quad \text{for }\lvert q\rvert<1.
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$$
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