Timeline for Does the ordinary generating function of Bell numbers converge?
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 6, 2021 at 4:03 | history | became hot network question | |||
| Jan 5, 2021 at 20:37 | comment | added | LSpice | Title of this article referenced by @darijgrinberg: Klazar - Bell numbers, their relatives, and algebraic differential equations. | |
| Jan 5, 2021 at 20:24 | answer | added | Qiaochu Yuan | timeline score: 9 | |
| Jan 5, 2021 at 20:22 | comment | added | Daniela | Thank you, that actually helped me! | |
| Jan 5, 2021 at 20:18 | comment | added | darij grinberg | Actually, the asymptotic expression for $\dfrac{\ln B_n}{n}$ ascribed to de Bruijn in en.wikipedia.org/wiki/Bell_number#Growth_rate should also preclude convergence of the series anywhere other than at $0$. | |
| Jan 5, 2021 at 20:11 | comment | added | darij grinberg | Are you referring to this article by Klazar? Because its Proposition 3.4 does make a (negative) claim about convergence, although maybe not the one you're looking for. My complex analysis has gotten really rusty, but I thought if a power series converges at some $z = z_0 \in \mathbb C$, then it should be analytic in the open ball of radius $\left|z_0\right|$ around $0$; is that true? If so, then I think it rules out convergence anywhere other than at $0$. | |
| Jan 5, 2021 at 20:03 | review | First posts | |||
| Jan 5, 2021 at 20:49 | |||||
| Jan 5, 2021 at 20:02 | history | asked | Daniela | CC BY-SA 4.0 |