Timeline for Simplify multiple sum involving rising factorials
Current License: CC BY-SA 4.0
25 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 3 at 17:51 | answer | added | Fred Hucht | timeline score: 2 | |
| Dec 3 at 11:22 | comment | added | Fred Hucht | @PeterTaylor There seems to be an error in your formula, it does not give the correct terms even for $a=b$. The error is in the last term of the $k$ sum. | |
| Dec 2 at 17:03 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Aug 4 at 17:00 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Apr 6 at 16:02 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Dec 8, 2023 at 16:00 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Aug 10, 2023 at 15:08 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Apr 12, 2023 at 15:00 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Dec 13, 2022 at 14:07 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Aug 15, 2022 at 13:07 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Apr 17, 2022 at 13:01 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Mar 18, 2022 at 12:37 | history | edited | Marcel | CC BY-SA 4.0 |
edited body
|
| Mar 14, 2022 at 16:00 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| S Feb 12, 2022 at 17:07 | history | bounty ended | CommunityBot | ||
| S Feb 12, 2022 at 17:07 | history | notice removed | CommunityBot | ||
| Feb 12, 2022 at 13:15 | answer | added | thedude | timeline score: 1 | |
| S Feb 4, 2022 at 15:21 | history | bounty started | Marcel | ||
| S Feb 4, 2022 at 15:21 | history | notice added | Marcel | Draw attention | |
| Feb 2, 2022 at 14:17 | history | edited | Marcel | CC BY-SA 4.0 |
deleted 3 characters in body
|
| Feb 2, 2022 at 14:03 | history | edited | Marcel | CC BY-SA 4.0 |
added 15 characters in body
|
| Feb 2, 2022 at 13:08 | history | edited | Marcel | CC BY-SA 4.0 |
added 191 characters in body
|
| Feb 1, 2022 at 22:51 | comment | added | Peter Taylor | Rephrasing it with $\binom{n}{k} = \frac{n_{(k)}}{k!}$ as $$f(x,y,a,b)= \sum_{m,n \geq 0} a^n b^m \sum_{i,r,q,l\ge 0}\frac{1}{(n+m+i+r+q+l+1)} \binom{x+i-1}{i}a^i \binom{y+r-1}{r}b^r \binom{y}{q} b^q \binom{x}{l}a^l \sum_{k=0}^{m+n} (-1)^k \binom{x+y+n+m+r+i-k}{n+m+r+i-k}^{-1} \binom{x+y+q+l+k-2}{q+l+k}^{-1}$$ doesn't give any immediate gain, as the sum on the right doesn't seem to be Zeilberger-summable, but might at least be a more recognisable form. | |
| Feb 1, 2022 at 18:16 | comment | added | Marcel | @CarloBeenakker It is in the format I want, but currently I have 6 infinite sums. I suspect some of them might be carried out explicitly. For instance, one might use the fact that $\sum_{i=0}^j\frac{(x)^{(i)}}{i!}=\frac{(x+1)^{(j)}}{j!}$. Notice the example I gave where 10 terms can be written as 3. | |
| Feb 1, 2022 at 18:08 | comment | added | Carlo Beenakker | your expression is already a series in powers of $a,b$; isn't that what you want? a more compact expression than what you have written down seems unlikely. | |
| Feb 1, 2022 at 17:58 | history | asked | Marcel | CC BY-SA 4.0 |