Showing LaTeX formulas in GitHub markdown.md

[terasakisatoshi]

Can we show math formula in GitHub ? The answer is yes.

This formula is generated via this app.

Here is my input:

\displaystyle  \left( \int_0^\infty \frac{\sin x}{\sqrt{x}} dx \right)^2 =   \sum_{k=0}^\infty \frac{(2k)!}{2^{2k}(k!)^2} \frac{1}{2k+1} =   \prod_{k=1}^\infty \frac{4k^2}{4k^2 - 1} = \frac{\pi}{2} 

References:

A hack for showing LaTeX formulas in GitHub markdown.md

[terasakisatoshi]

Examples

Matrix

\begin{bmatrix} \cos\theta && -\sin\theta \\ \sin\theta && \cos\theta \end{bmatrix}

Napier's Constant Limit Definition

• input:

\displaystyle \lim_{x\to\infty} \left(1+\frac{1}{n}\right)^n = e 

• output:

Transforming density functions

\displaystyle \begin{align*} p(y) &= \int_{-\infty}^\infty \delta(y-f(x)) q(x) dx, \quad f(x)=ax\\      &= \int_{-\infty}^\infty \delta(y-ax) q(x) dx \\      &= \int_{-\infty}^\infty \frac{1}{a}\delta(y-\tilde{x}) q\left(\frac{\tilde{x}}{a}\right) d\tilde{x} \\      &= \frac{1}{a}q\left(\frac{y}{a}\right) \end{align*}