Difference between revisions of "Dedekind eta"
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| − | Let $q=e^{2\pi i | + | Let $q=e^{2\pi i z}$, where $z$ is in the upper half plane. We define the Dedekind eta function by the formula |
$$\eta(\tau) = e^{\frac{\pi i \tau}{12}} \displaystyle\prod_{n=1}^{\infty} (1-q^n).$$ | $$\eta(\tau) = e^{\frac{\pi i \tau}{12}} \displaystyle\prod_{n=1}^{\infty} (1-q^n).$$ | ||
Revision as of 05:20, 12 February 2018
Let $q=e^{2\pi i z}$, where $z$ is in the upper half plane. We define the Dedekind eta function by the formula $$\eta(\tau) = e^{\frac{\pi i \tau}{12}} \displaystyle\prod_{n=1}^{\infty} (1-q^n).$$
Real part of $\eta$.
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
