Timeline for The geometric-mean factorial
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 1, 2014 at 12:26 | comment | added | Manfred Weis | Those generalized factorials can be interpreted as the length of paths in graphs; the integers would resemble the labels of vertices and the binary operation yields the weight of directed edges. My question related to shortest paths in the "Cantor Graph" originated in such an interpretation. One could now ask for shortest paths in the arithmetic-geometric mean graph and maybe obtain further interesting results. | |
| Dec 31, 2013 at 12:07 | vote | accept | Joseph O'Rourke | ||
| Dec 31, 2013 at 3:11 | comment | added | Suvrit | Actually the MathWorld link also suggests what the generalization of this function to real (or complex) arguments might be, e.g., by trying to solve $g(z+1)=zg(z)^2$ on wolframalpha.com | |
| Dec 31, 2013 at 1:59 | comment | added | Gerhard Paseman | In fact, the difference between $\sum_{1 \leq i \leq k} \log(i)/2^i$ and $\log(gm!(k+1))$ is sufficiently small that you might find the sum easier to handle. Gerhard "These Things Take A While" Paseman, 2013.12.30 | |
| Dec 31, 2013 at 1:28 | comment | added | Gerhard Paseman | The references provided by guest will likely have explored the following suggestion: Evaluate log of your constant as approximately .5078, or the limit of sum ln(i)/2^i . Gerhard "Adding Seems Simpler Than Multiplying" Paseman, 2013.12.30 | |
| Dec 31, 2013 at 1:22 | answer | added | guest | timeline score: 15 | |
| Dec 31, 2013 at 1:11 | history | asked | Joseph O'Rourke | CC BY-SA 3.0 |