Catalog of Series
From Qwiki
Since we do not know of any good web resources for looking up the solutions to challenging infinite series, we will use this page to list some of the more obscure ones that we come across. If you come across any that you also think are unusual, please put them here. Actually, this list could eventually become a catalog of lots of series, not just obscure ones. Put in whatever you want, along with some sort of reference!
Some series that arise in polymer physics
- (a Mabuchi Lab original): If
, then ![\sum_{p=1}^\infty \frac {1} {p^2} \cos^2\left[p \pi \alpha\right] = \frac{\pi^2}{2}\left(\alpha - \frac {1} {2} \right)^2 + \frac{\pi^2}{24}](/images/math/a/3/0/a30d4b835e59f7c47c15481656aeb7d1.png)
- (from The theory of polymer dynamics by Doi and Edwards). If
, then ![\sum_{p=1}^\infty \frac {1} {p^2} \left\{\cos\left[p \pi \alpha\right] - \cos\left[p \pi \beta\right] \right\}^2 = \frac{\pi^2}{2}|\alpha - \beta|](/images/math/6/9/7/697388ada1d23898256b96a53ad46bfe.png)
