Timeline for Is there any closed form expression for $\sum_{k=2}^\infty(-1)^k \left(- \frac{1}{2}\right)^{\frac{k(k+1)}{2}}$?
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| Oct 25, 2017 at 23:51 | comment | added | reuns | Incomplete theta functions are complicated, $\sum_{k=-\infty}^\infty(-1)^k k\ q^{\frac{k(k+1)}{2}}$ is a complete one. Is it possible to adapt your nested radical ? | |
| Oct 25, 2017 at 22:50 | history | edited | John Finkelstein | CC BY-SA 3.0 |
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| Oct 25, 2017 at 14:05 | comment | added | Nemo | It is called partial theta function. See formula $(1.6)$ in this article link.springer.com/article/10.1007/s11139-012-9370-1 , Kathrin Bringmann, Amanda Folsom, Robert C. Rhoades "Partial theta functions and mock modular forms as q-hypergeometric series". It does not have a closed form. | |
| Oct 25, 2017 at 13:34 | review | First posts | |||
| Oct 25, 2017 at 14:01 | |||||
| Oct 25, 2017 at 13:30 | history | asked | John Finkelstein | CC BY-SA 3.0 |