Scientific formulas

# Scientific Formulas

## Scientific Formula TeX (KaTeX)

MrDoc uses `KaTeX` to implement the function of writing mathematical formulas within documents. You can use an online formula editor to write formulas and then obtain their code:

<http://www.wiris.com/editor/demo/en/developers#mathml-latex>

![](/media//202005/2020-05-02_222616.png)

The following describes how to use formula code.

### Single-line Formula

If you need to write a single-line formula, you can wrap the formula with the `$$` symbol. The code is as follows:

```
$$E=mc^2$$
```

The above content will be rendered as the following formula:

$$E=mc^2$$

### Inline Formula

At the same time, single-line formulas support display within a line of text. The code is as follows:

```
行内的公式$$E=mc^2$$行内的公式，行内的$$E=mc^2$$公式。
```

The above content will be rendered as the following form:

行内的公式$$E=mc^2$$行内的公式，行内的$$E=mc^2$$公式。

Below are some more single-line formula examples:

```
$$x > y$$
```

$$x > y$$

```
$$$\sqrt{3x-1}+(1+x)^2$$$
```

$$$\sqrt{3x-1}+(1+x)^2$$$

```
$$\sin(\alpha)^{\theta}=\sum_{i=0}^{n}(x^i + \cos(f))$$
```

$$\sin(\alpha)^{\theta}=\sum_{i=0}^{n}(x^i + \cos(f))$$

- This is an inline formula in a list $$E=mc^2$$

| Table | Formula | Usage |
| --- | --- | --- |
| $$E=mc^2$$ |  |  |
| $$x > y$$ |  |  |
| $$$\sqrt{3x-1}+(1+x)^2$$$ |  |  |

### Multi-line Formula

Unlike single-line formulas, multi-line formulas require the use of triple-backtick code blocks. For example, the following code:

```math
	\displaystyle
	\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)
	```

will be rendered as the following formula:

```math
\displaystyle
\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)
```

Code:

```katex
	\displaystyle 
    	\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} }
        	} 
    	}
	```

will be rendered as the following formula:

```katex
\displaystyle 
    \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} }
        } 
    }
```

Code:

```latex
	f(x) = \int_{-\infty}^\infty
    	\hat f(\xi)\,e^{2 \pi i \xi x}
    	\,d\xi
	```

will be rendered as the following formula:

```latex
f(x) = \int_{-\infty}^\infty
    \hat f(\xi)\,e^{2 \pi i \xi x}
    \,d\xi
```