Synopsis

WikiPlugin to display mathematical formulae in a Wiki page.

Usage

<?plugin TeX2png text="$$(a+b)^n=\sum_{k=0}^n{n\choose k}a^k b^{n-k}$$" ?>

gives

$$(a+b)^n=\sum_{k=0}^n{n\choose k}a^k b^{n-k}$$

Arguments

There is only one argument which is the text of the mathematical expression. This text must be enclosed by a dollar $ within a paragraph or two dollars $$ on a separate line. In the last case, all is centered.

To write mathematical formulae, the syntax is the one of LaTeX.

Caveats

This plugin is only to produce readable mathematical formulae. Any other text is not allowed : so if an expression is not enclosed by dollars then it will be displayed by a red text. It is all the same possible to display raw text as $\textrm{\LaTeX}$ by using :

<?plugin TeX2png text="$\textrm{\LaTeX}$" ?>

This plugin is not able to produce sophisticated mathematicals texts with links, cross references... For that, you can use for example LaTeX2html.

Examples

Some Greeks letters : $\alpha$, $\beta$, ... and a formula $\sum_{i=1}^n \frac1{i^2}=\frac{\pi^2}{6}$ to test display in a paragraph.

Exercise 1 Consider the function

$$f(x)=(x^2-4x+3)^{1/2}$$

  1. Give the largest real domain for which f(x) is well defined.
  2. Give a domain on which the function is one-to-one. Using this domain derive a formula for the inverse function $f^{-1}(x)$.
  3. Calculate the derivative f'(x).

Exercise 2 Consider the function :

$$f(x) = \int_0^x e^{-t^2}\,dt, x\in\mathbb R$$
  1. Show that for all r > 0 :
    $$\frac{\pi}{2}\int_0^r t e^{-t^2}\,dt \leq \int_0^r e^{-x^2}\,dx \int_0^r e^{-y^2}\,dy \leq \frac{\pi}{2} \int_0^{\sqrt{2} r} t e^{-t^2}\,dt$$
    Help : you can use polar coordinates.
  2. Hence find the limit of $f(x)$ as x tends to $\infty$.

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