## Ramanujan Value of Ln(x) When X Tends to Zero

**Authors:** Jesús Sánchez

As we know, the natural logarithm at zero diverges, towards minus infinity:
lim┬(x→0)〖Ln(x)〗=-∞
But, as happens with other functions or series that diverge at some points, it has a Ramanujan or Cauchy principal value (a finite value) associated to that point. In this case, it will be calculated to be:
lim┬(x→0)〖Ln(x)〗=-γ
Being γ the Euler-Mascheroni constant 0.577215... It will be shown that Ln(0) tends to the negative of the sum of the harmonic series (that of course, diverges). But the harmonic series has a Cauchy principal value that is γ, the Euler-Mascheroni constant. So the finite associated value to Ln(0) will be calculated as - γ .

**Comments:** 3 Pages.

**Download:** **PDF**

### Submission history

[v1] 2019-04-06 08:36:03

**Unique-IP document downloads:** 24 times

Vixra.org is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary.
In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution.
Vixra.org will not be responsible for any consequences of actions that result from any form of use of any documents on this website.

**Add your own feedback and questions here:**

*You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.*

*
*