Difference between revisions of "Dedekind eta"

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=Properties=
 
=Properties=
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<strong>Theorem:</strong> The following formula holds for $\tau$ with $\mathrm{Im} \hspace{2pt} \tau > 0$:
 
$$\eta \left( -\dfrac{1}{\tau} \right) = (-i\tau)^{\frac{1}{2}}\eta(\tau).$$
 
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<strong>Proof:</strong> █
 
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=References=
 
=References=

Revision as of 19:51, 24 June 2016

Let $q=e^{2\pi i \tau}$. We define the Dedekind eta function by the formula $$\eta(\tau) = e^{\frac{\pi i \tau}{12}} \displaystyle\prod_{n=1}^{\infty} (1-q^n).$$

Properties

References

A collection of over 6200 identities for the Dedekind Eta Function