Timeline for iterated harmonic numbers vs Riemann zeta
Current License: CC BY-SA 3.0
16 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 19, 2017 at 1:00 | answer | added | Suvrit | timeline score: 3 | |
| Jun 18, 2017 at 19:20 | answer | added | GH from MO | timeline score: 10 | |
| Jun 18, 2017 at 19:15 | vote | accept | T. Amdeberhan | ||
| Jun 18, 2017 at 19:14 | comment | added | GH from MO | @Lewi_Sol: I think the identities recorded in these papers are not obscure but very general. | |
| Jun 18, 2017 at 19:12 | comment | added | Lewi_Sol | You may be right, but it seems obscure to me. | |
| Jun 18, 2017 at 19:08 | comment | added | GH from MO | @Lewi_Sol: See Theorem 4.2 in Hoffman's paper and Theorem 3.8 in Kawashima's paper. I am lazy to check all the details (how the identity in Question 2 follows from these). | |
| Jun 18, 2017 at 19:06 | comment | added | Lewi_Sol | Can you give reference pages? | |
| Jun 18, 2017 at 19:04 | comment | added | GH from MO | Regarding Question 2, I am quite certain the identity is a special case of an identity of Hoffman and Kawashima. See arxiv.org/abs/math/0702824 and arxiv.org/abs/math/0401319 | |
| Jun 18, 2017 at 18:57 | comment | added | François Brunault | This infinite sum can be expressed in terms of multiple zeta values. In the case $m=2$ we have $\sum_{n \geq 1} H_2(n)/n^2 = \zeta(2,1,1)+\zeta(3,1)+\zeta(4)+\zeta(2,2) = \zeta(4)+(1/4)\zeta(4)+\zeta(4)+(3/4)\zeta(4)=3\zeta(4)$ as you predicted (these relations date back essentially to Euler). | |
| Jun 18, 2017 at 18:42 | history | edited | T. Amdeberhan | CC BY-SA 3.0 |
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| Jun 18, 2017 at 18:30 | history | edited | T. Amdeberhan | CC BY-SA 3.0 |
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| Jun 18, 2017 at 18:30 | answer | added | Lucia | timeline score: 21 | |
| Jun 18, 2017 at 18:29 | comment | added | Sylvain JULIEN | If true, it would be a really beautiful formula. | |
| Jun 18, 2017 at 18:28 | comment | added | T. Amdeberhan | Quite extensively. | |
| Jun 18, 2017 at 18:23 | comment | added | ARG | how far did you check it numerically? | |
| Jun 18, 2017 at 17:40 | history | asked | T. Amdeberhan | CC BY-SA 3.0 |