# Questions tagged [theta-functions]

For questions about $\theta$ functions (special functions of several complex variables).

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### A sum related to the theta function

I am interested in the serie $$\sum_{n=1}^\infty(2n+1)e^{-tn(n+1)}$$ for something I am working on. Wolfram alpha gets stuck on this problem, but it gives the following result for a closely related ...
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### Mellin transform of theta function $\theta$ to show $\zeta(-1)=-\frac{1}{12}$

Edit: I realize a lot of attention is pointed at the proclamation $\zeta(-1)=-\frac{1}{12}$. Im more interested in the derivation of the Zeta function using the methods describe below, thank you! ...
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### $\sum_{n=1}^{\infty} \frac{\sin(n^2)}{n^2}$

Question: $$\sum_{n=1}^{\infty}\frac{\sin(n^2)}{n^2}=\,?$$ Previously I calculated a similar summation but it was more luck than wisdom, and insight led me to believe my methods were super incorrect (...
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### Can I express this sum as product of two theta functions?

I have an infinite sum written as $$\sum_{mn} e^{-i2\pi(m c_1 +n c_2)} e^{-(m^2+n^2-mn)}$$ where $m,n$ are integers, $0<c_1, c_2<1$. I want to express the above expression into a product of ...
1 vote
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