Timeline for Limit of an infinite series with quadratic arguments
Current License: CC BY-SA 4.0
13 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 22 at 17:32 | history | edited | Nemo | CC BY-SA 4.0 |
added reference
|
| Feb 18 at 2:27 | comment | added | Iosif Pinelis | Also, why the Gauss sums don't depend on $j$? I have just tried $n=5$, and then the sums do depend on $j$. | |
| Feb 18 at 2:25 | comment | added | Iosif Pinelis | Can you detail the second equality in your first proof (where $f$ first appears) and the use of the Poisson summation formula (?) in your second proof, where $\sum_{n=0}^a$ first appears? | |
| Feb 16 at 19:34 | history | edited | Nemo | CC BY-SA 4.0 |
thanks to Iosif Pinelis' observations, a typo is corrected, and a missing phase factor inserted
|
| Feb 16 at 18:49 | comment | added | Iosif Pinelis | Sorry for the delayed response. No, I don't have a better answer, and I don't think I ever implied anything like that. Concerning the first line of your first proof, I think there is at least one typo there. Concerning the first line of your second proof, I think the factor $(-1)^{-1/4}$ is missing on right-hand side there; hopefully, this does not affect the final result. | |
| Feb 15 at 7:12 | history | edited | Nemo | CC BY-SA 4.0 |
added proof without using Poisson summation
|
| Feb 15 at 5:28 | history | edited | Nemo | CC BY-SA 4.0 |
deleted 38 characters in body
|
| Feb 14 at 20:33 | comment | added | Iosif Pinelis | I think the formula is correct, but the manipulations with the delta functions need detalization/justification. I think answers are written not only for the OP, but also for their other readers -- so, they should be detailed enough in any case. | |
| Feb 14 at 6:07 | history | edited | Nemo | CC BY-SA 4.0 |
added 666 characters in body; added 3 characters in body; added 1 character in body
|
| Feb 14 at 5:53 | history | edited | Nemo | CC BY-SA 4.0 |
added info on calculation of the Gauss sum
|
| Feb 14 at 2:26 | comment | added | Iosif Pinelis | Previous comment continued: Mathematica does not know this identity even for $f=1$. | |
| Feb 13 at 22:24 | comment | added | Iosif Pinelis | Can you explain how the "(well known?) fact" is proved? | |
| Feb 13 at 7:16 | history | answered | Nemo | CC BY-SA 4.0 |