Timeline for continued fraction for logarithmic integral
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 24, 2021 at 2:26 | comment | added | Jesse Elliott | I now think the continued fraction actually diverges for $x > 1$, but I don't know how to prove this. | |
| May 16, 2021 at 20:58 | history | edited | Jesse Elliott | CC BY-SA 4.0 |
The expansions in the references are not known to be valid on the domain sought in the original post.
|
| May 5, 2021 at 20:50 | comment | added | Jesse Elliott | Again, (3.3.10) holds only for $|\operatorname{arg}(-\operatorname{Ln}(z)| < \pi$, which excludes the domain $x > 1$. Do you see the issue here? | |
| May 3, 2021 at 20:44 | comment | added | Jesse Elliott | This won't do it. The expansion for $\operatorname{Ei}(-z)$ is proved valid only for $|\operatorname{arg}(z)| < \pi$ and the expansion for $\operatorname{li}(z)$ for $|\operatorname{arg}(-\operatorname{Ln}(z))|< \pi$, which rules out the domain of $x > 1$ for $\operatorname{li}(x)$ that I'm interested in. (I actually have a copy of the book.) | |
| May 3, 2021 at 14:50 | comment | added | LSpice | The PDF link goes to the freely available "Back matter" of the Springer (re-?)issue of the referenced book. Here's a DOI link to the book: Lorentzen and Waadeland - Continued fractions - I. | |
| May 3, 2021 at 5:53 | history | answered | Alexey Ustinov | CC BY-SA 4.0 |