# Math Sample

## March 05, 2017 examplemath

KaTeX can be used to generate complex math formulas. It supports in-line math using the \$$... \$$ delimiters, like this: $$E = mc^2$$. By default, it does not support in-line delimiters $...$ because those occur too commonly in typical webpages. It supports displayed math using the $$ or \$...\$ delimiters, like this: Formula 1:$$ \phi = \frac{(1+\sqrt{5})}{2} = 1.6180339887\cdots $$Formula 2: (same formula, different delimiter) $\phi = \frac{(1+\sqrt{5})}{2} = 1.6180339887\cdots$ Additional details can be found on GitHub or on the Wiki. ### Example 1 If the text between$$ contains newlines it will rendered in display mode:

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


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

### Example 2

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


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

### Example 3

$$1 + \frac{q^2}{(1-q)}+\frac{q^6}{(1-q)(1-q^2)}+\cdots = \prod_{j=0}^{\infty}\frac{1}{(1-q^{5j+2})(1-q^{5j+3})}, \quad\quad \text{for }\lvert q\rvert<1.$$


$$1 + \frac{q^2}{(1-q)}+\frac{q^6}{(1-q)(1-q^2)}+\cdots = \prod_{j=0}^{\infty}\frac{1}{(1-q^{5j+2})(1-q^{5j+3})}, \quad\quad \text{for }\lvert q\rvert<1.$$

### Example 4

Remember, certain characters are rendered by markdown, so you may need to workaround those issues. You can find the complete list of KaTeX supported functions here: https://khan.github.io/KaTeX/docs/supported.html

For example, the ' character can be replaced with ^\prime:

$$G^\prime = G - u$$

The " character can be replaced with ^{\prime\prime}:

$$G^{\prime\prime} = G^\prime - v$$