Dedekind eta

From specialfunctionswiki
(Redirected from Dedekind eta function)
Jump to: navigation, search

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

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