Difference between revisions of "Dedekind eta"
From specialfunctionswiki
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| + | [[eta(z+1)=e^(i pi/12)eta(z)]]<br /> | ||
| + | [[eta(-1/z)=sqrt(-iz)eta(z)]]<br /> | ||
=References= | =References= | ||
Revision as of 05:17, 12 February 2018
Let $q=e^{2\pi i \tau}$. We define the Dedekind eta function by the formula $$\eta(\tau) = e^{\frac{\pi i \tau}{12}} \displaystyle\prod_{n=1}^{\infty} (1-q^n).$$
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
