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| <h1>WebKit MathML Demos (2016)</h1> |
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| <h2 id="math_fonts">Mathematical Fonts</h2> |
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| <p><math><semantics><mstyle displaystyle="true"><mi>γ</mi><mo>=</mo><mrow><munder><mo lspace="0em" rspace="0em">lim</mo><mrow><mi>n</mi><mo stretchy="false">→</mo><mn>∞</mn></mrow></munder><mrow><mo>(</mo><mrow><mo>−</mo><mo lspace="0em" rspace="thinmathspace">ln</mo><mi>n</mi><mo>+</mo><munderover><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></munderover><mfrac><mn>1</mn><mi>k</mi></mfrac></mrow><mo>)</mo></mrow></mrow><mo>=</mo><mrow><msubsup><mo>∫</mo><mn>1</mn><mn>∞</mn></msubsup><mrow><mo>(</mo><mrow><mfrac><mn>1</mn><mrow><mo stretchy="false">⌊</mo><mi>x</mi><mo stretchy="false">⌋</mo></mrow></mfrac><mo>−</mo><mfrac><mn>1</mn><mi>x</mi></mfrac></mrow><mo>)</mo></mrow><mspace width="thinmathspace"/><mi>d</mi><mi>x</mi></mrow><mo>≈</mo><mn>0.5772156649</mn></mstyle><annotation encoding="TeX">{\displaystyle \gamma = {\lim_{n\to \infty }\left(-\operatorname{ln} n+\sum _{k=1}^{n}{\frac {1}{k}}\right)} = {\int _{1}^{\infty }\left({\frac {1}{\lfloor x\rfloor }}-{\frac {1}{x}}\right)\,dx} \approx 0.5772156649}</annotation></semantics></math></p> |
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| <p><math class="libertinus"><semantics><mstyle displaystyle="true"><mi>γ</mi><mo>=</mo><mrow><munder><mo lspace="0em" rspace="0em">lim</mo><mrow><mi>n</mi><mo stretchy="false">→</mo><mn>∞</mn></mrow></munder><mrow><mo>(</mo><mrow><mo>−</mo><mo lspace="0em" rspace="thinmathspace">ln</mo><mi>n</mi><mo>+</mo><munderover><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></munderover><mfrac><mn>1</mn><mi>k</mi></mfrac></mrow><mo>)</mo></mrow></mrow><mo>=</mo><mrow><msubsup><mo>∫</mo><mn>1</mn><mn>∞</mn></msubsup><mrow><mo>(</mo><mrow><mfrac><mn>1</mn><mrow><mo stretchy="false">⌊</mo><mi>x</mi><mo stretchy="false">⌋</mo></mrow></mfrac><mo>−</mo><mfrac><mn>1</mn><mi>x</mi></mfrac></mrow><mo>)</mo></mrow><mspace width="thinmathspace"/><mi>d</mi><mi>x</mi></mrow><mo>≈</mo><mn>0.5772156649</mn></mstyle><annotation encoding="TeX">{\displaystyle \gamma = {\lim_{n\to \infty }\left(-\operatorname{ln} n+\sum _{k=1}^{n}{\frac {1}{k}}\right)} = {\int _{1}^{\infty }\left({\frac {1}{\lfloor x\rfloor }}-{\frac {1}{x}}\right)\,dx} \approx 0.5772156649}</annotation></semantics></math></p> |
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| <p><math style="font-family: STIXGeneral, STIXSizeOneSym, sans-serif"><semantics><mstyle displaystyle="true"><mi>γ</mi><mo>=</mo><mrow><munder><mo lspace="0em" rspace="0em">lim</mo><mrow><mi>n</mi><mo stretchy="false">→</mo><mn>∞</mn></mrow></munder><mrow><mo>(</mo><mrow><mo>−</mo><mo lspace="0em" rspace="thinmathspace">ln</mo><mi>n</mi><mo>+</mo><munderover><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></munderover><mfrac><mn>1</mn><mi>k</mi></mfrac></mrow><mo>)</mo></mrow></mrow><mo>=</mo><mrow><msubsup><mo>∫</mo><mn>1</mn><mn>∞</mn></msubsup><mrow><mo>(</mo><mrow><mfrac><mn>1</mn><mrow><mo stretchy="false">⌊</mo><mi>x</mi><mo stretchy="false">⌋</mo></mrow></mfrac><mo>−</mo><mfrac><mn>1</mn><mi>x</mi></mfrac></mrow><mo>)</mo></mrow><mspace width="thinmathspace"/><mi>d</mi><mi>x</mi></mrow><mo>≈</mo><mn>0.5772156649</mn></mstyle><annotation encoding="TeX">{\displaystyle \gamma = {\lim_{n\to \infty }\left(-\operatorname{ln} n+\sum _{k=1}^{n}{\frac {1}{k}}\right)} = {\int _{1}^{\infty }\left({\frac {1}{\lfloor x\rfloor }}-{\frac {1}{x}}\right)\,dx} \approx 0.5772156649}</annotation></semantics></math></p> |
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| <h2 id="hyperlinks">Hyperlinks</h2> |
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| <p><math display="block"><semantics><mrow href="https://en.wikipedia.org/wiki/Pythagorean_theorem"><mrow><msup><mi>a</mi><mn>2</mn></msup><mo>+</mo><msup><mi>b</mi><mn>2</mn></msup><mo>=</mo><msup><mi>c</mi><mn>2</mn></msup></mrow></mrow><annotation encoding="TeX">\href{https://en.wikipedia.org/wiki/Pythagorean_theorem}{a^2 + b^2 = c^2}</annotation></semantics></math></p> |
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| <p><math display="block"><semantics><mrow><mrow href="https://en.wikipedia.org/wiki/Legendre_symbol#Definition"><mrow><mo>(</mo><mfrac><mi>q</mi><mi>p</mi></mfrac><mo>)</mo></mrow></mrow><mrow><mo>(</mo><mfrac><mi>p</mi><mi>q</mi></mfrac><mo>)</mo></mrow><mo>=</mo><msup><mrow><mo stretchy="false">(</mo><mo>−</mo><mn>1</mn><mo stretchy="false">)</mo></mrow><mrow><mfrac><mrow><mi>p</mi><mo>−</mo><mn>1</mn></mrow><mn>2</mn></mfrac><mfrac><mrow><mi>q</mi><mo>−</mo><mn>1</mn></mrow><mn>2</mn></mfrac></mrow></msup></mrow><annotation encoding="TeX">\href{https://en.wikipedia.org/wiki/Legendre_symbol#Definition}{\left({\frac{q}{p}}\right)} \left({\frac {p}{q}}\right) = {(-1)}^{{\frac{p-1}{2}}{\frac{q-1}{2}}}</annotation></semantics></math></p> |
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| <p><math display="block"><semantics><mrow><mrow href="https://en.wikipedia.org/wiki/Determinant"><mo lspace="0em" rspace="0em">det</mo></mrow><mo stretchy="false">(</mo><mrow href="https://en.wikipedia.org/wiki/Matrix_exponential"><mrow><mo lspace="0em" rspace="0em">exp</mo><mi>A</mi></mrow></mrow><mo stretchy="false">)</mo><mo>=</mo><mo lspace="0em" rspace="0em">exp</mo><mrow><mo stretchy="false">(</mo><mrow href="https://en.wikipedia.org/wiki/Trace_(linear_algebr"><mrow><mstyle mathvariant="normal"><mrow><mi>T</mi><mi>r</mi></mrow></mstyle><mrow><mo stretchy="false">(</mo><mi>A</mi><mo stretchy="false">)</mo></mrow></mrow></mrow><mo stretchy="false">)</mo></mrow></mrow><annotation encoding="TeX">\href{https://en.wikipedia.org/wiki/Determinant}{\det}(\href{https://en.wikipedia.org/wiki/Matrix_exponential}{\exp{A}}) = \exp{(\href{https://en.wikipedia.org/wiki/Trace_(linear_algebr}{\mathrm{Tr}{(A)}})}</annotation></semantics></math></p> |
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| <h2 id="mathvariants">Mathvariants</h2> |
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| <p><math display="block"><semantics><mrow><mi>f</mi><mo>:</mo><mstyle mathvariant="fraktur"><mi>g</mi></mstyle><mo stretchy="false">→</mo><mstyle mathvariant="fraktur"><msup><mi>g</mi><mo>′</mo></msup></mstyle><mo>,</mo><mspace width="1em"/><mi>f</mi><mo stretchy="false">(</mo><mo stretchy="false">[</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo stretchy="false">]</mo><mo stretchy="false">)</mo><mo>=</mo><mo stretchy="false">[</mo><mi>f</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>,</mo><mi>f</mi><mo stretchy="false">(</mo><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">]</mo></mrow><annotation encoding="TeX">f:{\mathfrak {g}}\to {\mathfrak {g'}},\quad f([x,y])=[f(x),f(y)]</annotation></semantics></math></p> |
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| <p><math display="block"><semantics><mrow><msub><mstyle mathvariant="normal"><mrow><mi>S</mi><mi>L</mi></mrow></mstyle><mi>n</mi></msub><mo stretchy="false">(</mo><mstyle mathvariant="double-struck"><mi>R</mi></mstyle><mo stretchy="false">)</mo><mo>=</mo><mrow><mo>{</mo><mrow><mi>A</mi><mo>∊</mo><msub><mstyle mathvariant="script"><mi>M</mi></mstyle><mi>n</mi></msub><mo stretchy="false">(</mo><mstyle mathvariant="double-struck"><mi>R</mi></mstyle><mo stretchy="false">)</mo><mo>:</mo><mo lspace="0em" rspace="0em">det</mo><mi>A</mi><mo>=</mo><mn>1</mn></mrow><mo>}</mo></mrow></mrow><annotation encoding="TeX">{\mathrm{SL}}_n(\mathbb{R}) = \left\{ A \in \mathscr{M}_n(\mathbb{R}) : \det{A} = 1 \right\}</annotation></semantics></math></p> |
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| <p><math display="block"><semantics><mrow><mstyle mathvariant="double-struck"><mi>Z</mi></mstyle><mo>/</mo><mi>N</mi><mstyle mathvariant="double-struck"><mi>Z</mi></mstyle><mo>≅</mo><mstyle mathvariant="double-struck"><mi>Z</mi></mstyle><mo>/</mo><msub><mi>n</mi><mn>1</mn></msub><mstyle mathvariant="double-struck"><mi>Z</mi></mstyle><mo>×</mo><mo>⋯</mo><mo>×</mo><mstyle mathvariant="double-struck"><mi>Z</mi></mstyle><mo>/</mo><msub><mi>n</mi><mi>k</mi></msub><mstyle mathvariant="double-struck"><mi>Z</mi></mstyle></mrow><annotation encoding="TeX">{\mathbb {Z}}/N{\mathbb {Z}}\cong {\mathbb {Z}}/n_{1}{\mathbb {Z}}\times \cdots \times {\mathbb {Z}}/n_{k}{\mathbb {Z}}</annotation></semantics></math></p> |
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| <h2 id="operators">Operators</h2> |
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| <p><math display="block"><semantics><mrow><msup><mrow><mo>(</mo><mroot><mn>2</mn><mn>3</mn></mroot><mo>)</mo></mrow><mi>N</mi></msup><mo>=</mo><munder><munder><mrow><mroot><mn>2</mn><mn>3</mn></mroot><mo>×</mo><mroot><mn>2</mn><mn>3</mn></mroot><mo>×</mo><mroot><mn>2</mn><mn>3</mn></mroot><mo>×</mo><mo>…</mo><mo>×</mo><mroot><mn>2</mn><mn>3</mn></mroot></mrow><mo>⏟</mo></munder><mrow><mi>N</mi><mspace width="thinmathspace"/><mtext>times</mtext></mrow></munder><mo>=</mo><msup><mn>2</mn><mrow><mi>N</mi><mo>/</mo><mn>3</mn></mrow></msup></mrow><annotation encoding="TeX">\left(\sqrt[3]{2}\right)^N = \underset{N\,\text{times}}{\underbrace{\sqrt[3]{2} \times \sqrt[3]{2} \times \sqrt[3]{2} \times \dots \times \sqrt[3]{2}}} = 2^{N/3}</annotation></semantics></math></p> |
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| <p><math display="block"><semantics><mrow><mrow><mi>Γ</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></mrow><mo>=</mo><munder><mo lspace="0em" rspace="0em">lim</mo><mrow><mi>n</mi><mo stretchy="false">→</mo><mn>∞</mn></mrow></munder><mspace width="thinmathspace"/><mfrac><mrow><mi>n</mi><mo>!</mo><mspace width="thickmathspace"/><msup><mi>n</mi><mi>t</mi></msup></mrow><mrow><mi>t</mi><mspace width="thickmathspace"/><mo stretchy="false">(</mo><mi>t</mi><mo>+</mo><mn>1</mn><mo stretchy="false">)</mo><mo>⋯</mo><mo stretchy="false">(</mo><mi>t</mi><mo>+</mo><mi>n</mi><mo stretchy="false">)</mo></mrow></mfrac><mo>=</mo><mfrac><mn>1</mn><mi>t</mi></mfrac><munderover><mo>∏</mo><mrow><mi>n</mi><mo>=</mo><mn>1</mn></mrow><mn>∞</mn></munderover><mfrac><msup><mrow><mo>(</mo><mrow><mn>1</mn><mo>+</mo><mfrac><mn>1</mn><mi>n</mi></mfrac></mrow><mo>)</mo></mrow><mi>t</mi></msup><mrow><mn>1</mn><mo>+</mo><mfrac><mi>t</mi><mi>n</mi></mfrac></mrow></mfrac><mo>=</mo><mfrac><msup><mi>e</mi><mrow><mo>−</mo><mi>γ</mi><mi>t</mi></mrow></msup><mi>t</mi></mfrac><munderover><mo>∏</mo><mrow><mi>n</mi><mo>=</mo><mn>1</mn></mrow><mn>∞</mn></munderover><msup><mrow><mo>(</mo><mrow><mn>1</mn><mo>+</mo><mfrac><mi>t</mi><mi>n</mi></mfrac></mrow><mo>)</mo></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup><msup><mi>e</mi><mfrac><mi>t</mi><mi>n</mi></mfrac></msup></mrow><annotation encoding="TeX">{\Gamma(t)} = \lim_{n \to \infty}\, \frac{n! \; n^t}{t \; (t+1)\cdots(t+n)}= \frac{1}{t} \prod_{n=1}^\infty \frac{\left(1+\frac{1}{n}\right)^t}{1+\frac{t}{n}} = \frac{e^{-\gamma t}}{t} \prod_{n=1}^\infty \left(1 + \frac{t}{n}\right)^{-1} e^{\frac{t}{n}}</annotation></semantics></math></p> |
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| <h2 id="displaystyle">Displaystyle</h2> |
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| <p><math><semantics><mrow><mrow><mrow><munderover><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow><mrow><mo>+</mo><mn>∞</mn></mrow></munderover><mfrac><mn>9</mn><msup><mi>k</mi><mn>4</mn></msup></mfrac></mrow><mo>=</mo><mfrac><msup><mi>π</mi><mn>4</mn></msup><mn>10</mn></mfrac></mrow><mo>=</mo><mstyle displaystyle="true"><mfrac><msup><mi>π</mi><mn>4</mn></msup><mn>10</mn></mfrac><mo>=</mo><mrow><munderover><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow><mrow><mo>+</mo><mn>∞</mn></mrow></munderover><mfrac><mn>9</mn><msup><mi>k</mi><mn>4</mn></msup></mfrac></mrow></mstyle></mrow><annotation encoding="TeX">{{\sum_{k=1}^{+\infty} \frac{9}{k^4}} = \frac{\pi^4}{10}} = {\displaystyle \frac{\pi^4}{10} = {\sum_{k=1}^{+\infty} \frac{9}{k^4}}}</annotation></semantics></math></p> |
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| <p><math display="block"><semantics><mstyle displaystyle="true"><mstyle mathvariant="bold"><mi>B</mi></mstyle><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mo>=</mo><mfrac><mrow><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>0</mn></mrow><mi>n</mi></munderover><msub><mi>b</mi><mrow><mi>i</mi><mo>,</mo><mi>n</mi></mrow></msub><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><msub><mstyle mathvariant="bold"><mi>P</mi></mstyle><mi>i</mi></msub><msub><mi>w</mi><mi>i</mi></msub></mrow><mrow><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>0</mn></mrow><mi>n</mi></munderover><msub><mi>b</mi><mrow><mi>i</mi><mo>,</mo><mi>n</mi></mrow></msub><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><msub><mi>w</mi><mi>i</mi></msub></mrow></mfrac></mstyle><annotation encoding="TeX">{\displaystyle \mathbf {B} (t)={\frac {\sum _{i=0}^{n}b_{i,n}(t)\mathbf {P} _{i}w_{i}}{\sum _{i=0}^{n}b_{i,n}(t)w_{i}}}}</annotation></semantics></math></p> |
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| <p><math display="block"><semantics><mrow><msup><mrow><mo>(</mo><mrow><munderover><mo>∏</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></munderover><msup><mi>A</mi><mi>i</mi></msup></mrow><mo>)</mo></mrow><mn>2</mn></msup><mo>=</mo><msup><mrow><mo>(</mo><msup><mi>A</mi><mrow><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></munderover><mi>i</mi></mrow></msup><mo>)</mo></mrow><mn>2</mn></msup><mo>=</mo><msup><mi>A</mi><mrow><mi>n</mi><mrow><mo stretchy="false">(</mo><mi>n</mi><mo>−</mo><mn>1</mn><mo stretchy="false">)</mo></mrow></mrow></msup></mrow><annotation encoding="TeX">\left(\prod_{i=1}^n A^i\right)^2 = \left(A^{\sum_{i=1}^n i}\right)^2 = A^{n{(n-1)}}</annotation></semantics></math></p> |
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| <h2 id="open_type_math_parameters">OpenType MATH Parameters</h2> |
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| <p><math display="block"><semantics><mstyle displaystyle="true"><mi>π</mi><mo>=</mo><mstyle displaystyle="true"><mfrac><mn>4</mn><mrow><mn>1</mn><mo>+</mo><mstyle displaystyle="true"><mfrac><msup><mn>1</mn><mn>2</mn></msup><mrow><mn>2</mn><mo>+</mo><mstyle displaystyle="true"><mfrac><msup><mn>3</mn><mn>2</mn></msup><mrow><mn>2</mn><mo>+</mo><mstyle displaystyle="true"><mfrac><msup><mn>5</mn><mn>2</mn></msup><mrow><mn>2</mn><mo>+</mo><mo>⋱</mo></mrow></mfrac></mstyle></mrow></mfrac></mstyle></mrow></mfrac></mstyle></mrow></mfrac></mstyle><mo>=</mo><munderover><mo>∑</mo><mrow><mi>n</mi><mo>=</mo><mn>0</mn></mrow><mn>∞</mn></munderover><mfrac><mrow><mn>4</mn><mo stretchy="false">(</mo><mo>−</mo><mn>1</mn><msup><mo stretchy="false">)</mo><mi>n</mi></msup></mrow><mrow><mn>2</mn><mi>n</mi><mo>+</mo><mn>1</mn></mrow></mfrac><mo>=</mo><mfrac><mn>4</mn><mn>1</mn></mfrac><mo>−</mo><mfrac><mn>4</mn><mn>3</mn></mfrac><mo>+</mo><mfrac><mn>4</mn><mn>5</mn></mfrac><mo>−</mo><mfrac><mn>4</mn><mn>7</mn></mfrac><mo>+</mo><mo>−</mo><mo>⋯</mo></mstyle><annotation encoding="TeX">{\displaystyle \pi ={\displaystyle \frac{4}{1+{\displaystyle \frac {1^{2}}{2+{\displaystyle \frac {3^{2}}{2+{\displaystyle \frac {5^{2}}{2+\ddots }}}}}}}}=\sum _{n=0}^{\infty }{\frac {4(-1)^{n}}{2n+1}}={\frac {4}{1}}-{\frac {4}{3}}+{\frac {4}{5}}-{\frac {4}{7}}+-\cdots }</annotation></semantics></math></p> |
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| <p><math display="block"><semantics><mrow><msub><mstyle mathvariant="normal"><mi>Φ</mi></mstyle><mi>E</mi></msub><mo>=</mo><mrow><msub><mo>∯</mo><mi>S</mi></msub><mstyle mathvariant="bold"><mi>E</mi></mstyle><mo>⋅</mo><mstyle mathvariant="normal"><mi>d</mi></mstyle><mstyle mathvariant="bold"><mi>A</mi></mstyle></mrow><mo>=</mo><mfrac><mi>Q</mi><msub><mi>ϵ</mi><mn>0</mn></msub></mfrac></mrow><annotation encoding="TeX">{\mathrm \Phi}_E = {\oiint_S \mathbf {E} \cdot \mathrm{d} \mathbf{A}} = \frac{Q}{\epsilon_0}</annotation></semantics></math></p> |
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| <h2 id="arabic_mathematics">Arabic Mathematics</h2> |
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| <p dir="rtl"> |
| <math class="arabic" dir="rtl" display="block"> |
| <mmultiscripts> |
| <mo>ل</mo> |
| <mi>𞸟</mi> |
| <none></none> |
| <mprescripts></mprescripts> |
| <none></none> |
| <mi>𞸝</mi> |
| </mmultiscripts> |
| <mo>=</mo> |
| <mrow> |
| <mfrac> |
| <mi>𞸝</mi> |
| <mi>𞸟</mi> |
| </mfrac> |
| <mmultiscripts> |
| <mo>ل</mo> |
| <mrow> |
| <mi>𞸟</mi> |
| <mo>−</mo> |
| <mn>١</mn> |
| </mrow> |
| <none></none> |
| <mprescripts></mprescripts> |
| <none></none> |
| <mrow> |
| <mi>𞸝</mi> |
| <mo>−</mo> |
| <mn>١</mn> |
| </mrow> |
| </mmultiscripts> |
| </mrow> |
| </math> |
| </p> |
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| <p dir="rtl"><math class="arabic" dir="rtl" display="block"><semantics><mrow><mi>س</mi><mo>=</mo><mfrac><mrow><mo>−</mo><mi>ب</mi><mo>±</mo><msqrt><mrow><msup><mi>ب</mi><mn>٢</mn></msup><mo>−</mo><mn>٤</mn><mi>ا</mi><mi>ج</mi></mrow></msqrt></mrow><mrow><mn>٢</mn><mi>ا</mi></mrow></mfrac></mrow><annotation encoding="TeX">س = \frac{-ب\pm\sqrt{ب^٢-٤اج}}{٢ا}</annotation></semantics></math></p> |
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| </body> |
| </html> |
