Dedekind eta

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

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  Real part of $\eta$.

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  Imaginary part of $\eta$.

Properties

eta(z+1)=e^(i pi/12)eta(z)
eta(-1/z)=sqrt(-iz)eta(z)

References

A collection of over 6200 identities for the Dedekind Eta Function