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<title>MathML Examples</title>
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<h1>Use of the Ruby Module with MathML</h1>
<h2 class="display">William F. Hammond</h2>
<p class="display">Copyright &copy; 2001 William F. Hammond</p>

<p>
This is an XHTML document that uses the MathML and Ruby extensions of
basic XHTML markup.
</p>
<p>
The square of x is entered here using MathML:
<ruby><rb><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>2</mn></msup></math></rb><rp class="blankout"> &nbsp;&nbsp;[If you see
this text, your browser needs updating in order to handle one or both of
CSS and the XHTML Ruby module.]</rp><rt>-- TeX source: "x^2".</rt><rp></rp></ruby>
</p>
<p>
Here is a displayed form of the Weierstrass infinite product expansion
of the gamma function.
</p>
<p><ruby><rb><math xmlns="http://www.w3.org/1998/Math/MathML" class="display" mode="display"><mrow>
 <mrow>
  <msubsup><mo>&Integral;</mo><mrow><mn>0</mn></mrow><mi>&infin;</mi></msubsup><mrow>
   <msup><mrow><mi>t</mi></mrow><mrow><mi>x</mi></mrow></msup> <mo> </mo> <msup><mrow><mi>e</mi></mrow><mrow><mi>-t</mi></mrow></msup> <mo> </mo>
   <mfrac><mrow><mi>dt</mi></mrow><mi>t</mi></mfrac>
  </mrow>
 </mrow><mo>=</mo><mrow>
  <mfrac><mrow><mn>1</mn></mrow><mrow><mi>x</mi></mrow></mfrac> <mo> </mo>
  <msubsup><mo>&Product;</mo><mrow><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow></mrow><mi>&infin;</mi></msubsup><mrow>
   <mrow>
    <mfrac><mrow>
     <msup><mrow><mfenced><mrow><mn>1</mn><mo>+</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mi>k</mi></mrow></mfrac></mrow></mfenced></mrow><mrow><mi>x</mi></mrow></msup>
    </mrow><mrow>
     <mfenced><mrow><mn>1</mn><mo>+</mo><mfrac><mrow><mi>x</mi></mrow><mrow><mi>k</mi></mrow></mfrac></mrow></mfenced>
    </mrow></mfrac>
   </mrow>
  </mrow>
 </mrow>
</mrow></math></rb><rp></rp><rt><br /><br />
[If the MathML markup above does not render in your browser, consult
<a href="gamma-iden.gif">this
image</a> or decipher the following equivalent pseudo-TeX source:<br />
\int_0^{\infty} t^x e^{-t} dt/t = <br />
(1/x) \prod_{k=1}^{\infty}
\frac{(1 + 1/k)^x}{1 + x/k} ]<br />
</rt><rp></rp></ruby></p>

<p>
This web page is offered as an example of a fully functioning
XHTML 1.1 plus MathML 2.0 document that is both safe and usable
in a wide array of legacy web browsers such as NetScape 4.5 and
lynx 2.8 (rel 2).
</p>
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