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As I am introducing LaTeX to an audience, I'd like to show how it can render equations beautifully. As such, I'd like one equation (math/physics) that combines many different formatting requirements, such as integrals, sums, greek, other fonts, maybe even matrices.

This is (closely) secondary but it would be good if the equation had some theoretical significance. It would also be interesting if it involved matrices, but I don't think that's very possible.

Edit: For now, I have chosen the following equation, a functional equation that is crucial in the proof of the Prime Number Theorem:

Functional equation crucial in the proof of the Prime Number Theorem

If anyone has a better equation, please answer below! I'd love a better one.

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For an audience presentation I'd recommend several small examples each displaying one or two cool TeX formatting features. Then you could finish with a single long one. I would also recommend genuine significant examples rather than artificial constructs. –  Ethan Bolker Feb 20 '13 at 14:40
    
My presentation is very brief, so I'd like a single long one with some significance, as requested in my question. –  Herng Yi Feb 20 '13 at 15:00
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2 Answers 2

You might want to take a look at Jeff Tupper's self-referential formula (link) or its derivatives (link). Or you may consider throwing in a little String Theory (link). Strictly speaking it might not be mathematics but it's still nice.

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See http://mirror.ctan.org/info/math/voss/mathmode/Mathmode.pdf for a lot of examples for inline and display math mode. Anotherone for using an OpenType math font is http://www.tug.org/store/lucida/lucida-amsmath.pdf The source is also available.

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Thanks, but these examples are all too simple. I would like to exhibit many capabilities in one single equation. –  Herng Yi Feb 20 '13 at 11:30
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