Including mathematical formulae into AniWiki

Including mathematical formulae into AniWiki

Based on the math plugin, I created a method for AniWiki to generate mathematical formulae, which is fairly similar to TeX/LaTeX.

Syntax

Dokuwiki Syntax:

$...text style mathematical formula...$
$$...display style mathematical formula...$$

I don't think I still need to explain what are textstyle and displaystyle in LaTeX. See the examples below.

Download

My modified version of the plugin is here: mathmulti.zip (1.2K)

Example

Let's try the familiar CLT formula here.

Stronger form of the Central Limit Theorem

Let $\normalsize X_{1}, X_{2}, \ldots$ be a sequence of iid random variables with $\normalsize E(X_{i})=\mu$ and $\normalsize 0<Var(X_i)=\sigma^2<\infty$ . Define $\normalsize \bar{X}_n=(1/n)\sum_{i=1}^n X_i$ . Let $\normalsize G_n(x)$ denote the cdf of $\normalsize \sqrt{n}(\bar{X}_n-\mu)/\sigma$ . Then, for any $\normalsize x$ , $\normalsize -\infty<x<\infty$ ,

$\lim_{n\rightarrow\infty}G_n(x)=\int_{-\infty}^x \frac{1}{\sqrt{2\pi}}e^{-y^2/2}dy$

that is, $\normalsize \sqrt{n}(\bar{X}_n-\mu)/\sigma$ has a limiting standard normal distribution.

Let $X_{1}, X_{2}, \ldots$ be a sequence of iid random variables with $E(X_{i})=\mu$ 
and $0<Var(X_i)=\sigma^2<\infty$. Define $\bar{X}_n=(1/n)\sum_{i=1}^n X_i$. 
Let $G_n(x)$ denote the cdf of $\sqrt{n}(\bar{X}_n-\mu)/\sigma$. 
Then, for any $x$, $-\infty<x<\infty$,

$$\lim_{n\rightarrow\infty}G_n(x)=\int_{-\infty}^x \frac{1}{\sqrt{2\pi}}e^{-y^2/2}dy$$

that is, $\sqrt{n}(\bar{X}_n-\mu)/\sigma$ has a limiting standard normal distribution.

Taylor series

This formula is familiar for us:

$f(x) = f(a) + \frac{f'(a)}{1!}(x - a) + \frac{f^{(2)}(a)}{2!}(x - a)^2 + \cdots + \frac{f^{(n)}(a)}{n!}(x - a)^n + R_n(x)$

$$f(x) = f(a) + \frac{f'(a)}{1!}(x - a) + \frac{f^{(2)}(a)}{2!}(x - a)^2 
       + \cdots + \frac{f^{(n)}(a)}{n!}(x - a)^n + R_n(x)$$