Timeline for Does the ordinary generating function of Bell numbers converge?
Current License: CC BY-SA 4.0
7 events
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| Jan 5, 2021 at 23:27 | history | edited | Qiaochu Yuan | CC BY-SA 4.0 |
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| Jan 5, 2021 at 21:24 | history | edited | Qiaochu Yuan | CC BY-SA 4.0 |
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| Jan 5, 2021 at 21:24 | comment | added | Qiaochu Yuan | @Ira: yes! The second one should follow from the fact that $B_n$ is the sequence of moments of the Poisson distribution (with $\lambda = 1$). I got nothing on the first one though. | |
| Jan 5, 2021 at 21:11 | comment | added | Ira Gessel | We also have continued fractions for $B(x) = \sum_{n=0}^\infty B_n x^n$: $$B(x) = \cfrac{1}{1- \cfrac{x}{1- \cfrac{x}{1- \cfrac{x}{1- \cfrac{2x}{1- \cfrac{x}{1- \cfrac{3x}{1- \cfrac{x}{1- \cfrac{4x}{1-\cdots }}}}}}}}} $$ and $$B(x) = \cfrac{1}{1-x- \cfrac{x^2}{1-2x- \cfrac{2x^2}{1-3x- \cfrac{3x^2}{1-\cdots }}}} $$ | |
| Jan 5, 2021 at 20:46 | history | edited | Qiaochu Yuan | CC BY-SA 4.0 |
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| Jan 5, 2021 at 20:31 | history | edited | Qiaochu Yuan | CC BY-SA 4.0 |
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| Jan 5, 2021 at 20:24 | history | answered | Qiaochu Yuan | CC BY-SA 4.0 |