Timeline for closed form for an alternating cosecant sum
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| 5 hours ago | history | became hot network question | |||
| 8 hours ago | comment | added | Alexey Ustinov | This sum is some kind of error term. If we express linear function $f(x)=x$ as a finite Fourier series (FFS) (using values at integer points), then this sum will be the value of FFS at half-integer point. | |
| 10 hours ago | answer | added | Fred Hucht | timeline score: 2 | |
| 11 hours ago | answer | added | Carlo Beenakker | timeline score: 3 | |
| 11 hours ago | comment | added | Iosif Pinelis | Mathematica cannot do anything with this sum. So, it is unlikely to have a closed-form expression. | |
| 12 hours ago | comment | added | Martin M. W. | One idea might be to use the Euler reflection formula to write $$ \frac{(-1)^j}{\sin\left(\frac{\pi j}{n}\right)} = \frac{(-1)^j \Gamma\left(\frac{j}{n}\right) \Gamma\left(1-\frac{j}{n}\right)}{\pi}. $$ and look for an expression in terms of a hypergeometric series. | |
| 13 hours ago | history | asked | Slm2004 | CC BY-SA 4.0 |