Timeline for Sequences that sum up to possible generalization of Euler or up/down numbers (A000111)
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 8, 2023 at 7:38 | comment | added | Peter Taylor | Just take $k$th roots. You can do it by substituting and doing a lot of algebra, but it ends up in the same place. | |
| Jun 7, 2023 at 17:32 | comment | added | Notamathematician | @PeterTaylor, if you substitute your result into the original formula, is it possible to get a closed form? | |
| Jun 7, 2023 at 14:35 | comment | added | Notamathematician | @PeterTaylor, thank you again! I'm too lazy to figure it out myself, so I'll try to ask around from familiar experts. | |
| Jun 7, 2023 at 14:32 | comment | added | Peter Taylor | There does appear to be support for number fields in PARI, but I don't use PARI and I don't know whether that page contains sufficient information on how to calculate with elements of number fields. | |
| Jun 7, 2023 at 14:19 | comment | added | Notamathematician | @PeterTaylor, thank you for comment! Nice observation! Could you tell me how to calculate the square root on PARI so that when extracting the coefficient from the function, an integer result is obtained? I tried c^(1/2) but for large $k$ it still turns out to be a decimal fraction. | |
| Jun 6, 2023 at 15:05 | comment | added | Peter Taylor | Note that unless $k = 2m$, $$A(x)^k = \frac{2(2m-k)(m-k+\alpha) e^{\alpha x}}{((m-k+\alpha) e^{\alpha x} + m)^2}$$ with $\alpha = \sqrt{k^2 - 2km}$ | |
| Jun 3, 2023 at 23:54 | history | edited | Michael Hardy | CC BY-SA 4.0 |
added 6 characters in body
|
| Jun 3, 2023 at 13:27 | history | asked | Notamathematician | CC BY-SA 4.0 |