Timeline for Bounds for $\sum_{k=1}^\infty\frac{(-1)^{k+1}x^k}{(k-1)!\zeta(2k)}$
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 8, 2013 at 14:45 | vote | accept | joro | ||
| Jun 3, 2013 at 18:05 | answer | added | Noam D. Elkies | timeline score: 16 | |
| Jun 3, 2013 at 17:42 | comment | added | David E Speyer | Ah, thank you! And math.upenn.edu/~wilf/website/RieszFunction.pdf proves that the Riesz function has infinitely many real zeroes, showing that the numeric evidence is misleading. | |
| Jun 3, 2013 at 17:39 | answer | added | David E Speyer | timeline score: 9 | |
| Jun 3, 2013 at 16:46 | comment | added | Barry Cipra | The OP is asking about the Riesz function, en.wikipedia.org/wiki/Riesz_function | |
| Jun 3, 2013 at 14:13 | comment | added | Brendan McKay | I used Maple with 1000 digit precision. It gets quite hard to compute when $x$ is large, at least by brute summation. Probably there is some sequence accelerator that helps. | |
| Jun 3, 2013 at 14:07 | comment | added | joro | Brendan thank you. This agrees with mpmath's plots. What software are you using? btw, not sure if these numeric results are correct, mpmath occasionally gives provably wrong result on alternating sums... | |
| Jun 3, 2013 at 13:23 | comment | added | Brendan McKay | Starts at 0, local max of about 0.125 at about x=0.48, crosses zero about 1.15, local min of about -0.82 at about 7.1, then slowly tends to 0 from below. | |
| Jun 3, 2013 at 12:18 | history | asked | joro | CC BY-SA 3.0 |