MathML Examples

William F. Hammond

This is an XHTML document with MathML markup prepared using the basic layer of GELLMU and the XML namespaces regime for extending the basic tagset of XHTML.

The following relation is sometimes called the parallelogram law.

{||a||}^{2} + {||b||}^{2} = \frac{1}{2} \{{||a + b||}^{2} + {||a - b||}^{2}\}

Balancers should be stretched when appropriate. Here the simple fraction $1 / 2$ is multiplied with a complex fraction.

\frac{1}{2} \{\frac{\frac{a}{b}}{\frac{c}{d}}\}

This is MathML markup of the formula for the roots of the quadratic polynomial $a x^{2} + b x + c$ .

x = \frac{- b \pm {(b^{2} - 4 a c)}^{1 / 2}}{2 a}

This is MathML markup for a 2 × 2 matrix.

A = [\begin{matrix} a & b \\ c & d \end{matrix}]

Taylor's Theorem:

f (x) = \sum_{j = 0}^{\infty}  \frac{f^{(j)} (0)}{j!} x^{j}

This is a form of the Weierstrass infinite product expansion of the gamma function.

\int_{0}^{\infty} t^{x} e^{-t} \frac{dt}{t} =  \frac{1}{x} \prod_{k = 1}^{\infty} \frac{{(1 + \frac{1}{k})}^{x}}{(1 + \frac{x}{k})}

Dirac's $δ$ -function, which is actually a distribution in the sense of L. Schwartz rather than a function, is characterized by the property that for every $C^{\infty}$ function $f$ with compact support one has:

\int_{- \infty}^{\infty} f δ = f (0) .

In particular, when $f$ is the characteristic function $I_{S}$ of a set $S$ :

\int_{S}^{} δ = \{\begin{matrix} 1 & if S contains 0 . \\ 0 & otherwise. \end{matrix}