Timeline for Identity involving double sum with binomials
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 9, 2022 at 15:52 | comment | added | Max Alekseyev | @Marcel: Caring about integrals convergence makes calculation somewhat cumbersome (with triple instead of double integrals), and I was not patient enough to work out details. I'm still trying to find a shortcut though. | |
| Feb 9, 2022 at 14:58 | comment | added | Marcel | @MaxAlekseyev I put the bounty. Did you find the time to address the $b\ge x$ point? | |
| Jan 28, 2022 at 16:50 | comment | added | Max Alekseyev | @IosifPinelis: I think we need to replace $(x-b)^{(B+b)}$ with $(-1)^{B+b} (B+b)! \binom{b-x}{B+b}$. I'm pretty sure the idea still works in this setting. I'll try to rewrite it more accurately. | |
| Jan 28, 2022 at 16:38 | comment | added | Iosif Pinelis | However large $x$ is, $b$ can be larger than $x$. I guess some modification of your proof is needed. | |
| Jan 28, 2022 at 16:33 | comment | added | Iosif Pinelis | If $b\ge x$, then the corresponding beta integral is infinite. How do you deal with this? | |
| Jan 28, 2022 at 16:32 | comment | added | Marcel | Wow, that's some calculation. Thanks, I will put a bounty on it when it is allowed. | |
| Jan 28, 2022 at 16:27 | history | edited | Max Alekseyev | CC BY-SA 4.0 |
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| Jan 28, 2022 at 16:21 | history | answered | Max Alekseyev | CC BY-SA 4.0 |