LOG#162. Polylogia flashes(IV).

In this final post (by the moment) in the polylogia series we will write some additional formulae for polylogs and associated series. Firstly, we have (1)   and now, if (2)   (3)   The next identity also holds   … Continue reading

LOG#161. Polylogia flashes(III).

In the third post of this series I will write more fantastic identities related to our friends, the polylogs! (1)   and by analytic continuation that equation can be extended to all . In fact (2)   such as , … Continue reading

LOG#160. Polylogia flashes(II).

The polylogarithm or Jonquière’s function is generally defined as     Do not confuse with the logarithm integral in number theory, which is     such as     and     . In fact, notation can be confusing sometimes … Continue reading

LOG#159. Polylogia flashes (I).

In the next series of post, I am going to define (again) and write some cool identities of several objects that mathematicians and physicists know as zeta functions and polylogarithms. I have talked about them already here http://www.thespectrumofriemannium.com/2012/11/07/log051-zeta-zoology/ 1. We … Continue reading

LOG#158. Ramanujan’s equation.

Hi, everyone! I am back, again! And I have some new toys in order to post faster (new powerful plugin). Topic today: Ramanujan! Why Ramanujan liked the next equation? (1)   This equation can be rewritten as follows (2)   … Continue reading

LOG#157. Superstatistics (II).

Following the previous article, now I will discuss some interesting points in the paper: Generalized information entropies depending only on the probability distribution, by O.Obregón and A.Gil-Villegas. You can find the paper here http://arxiv.org/abs/1206.3353 The Boltzmann factor for a generalized … Continue reading

LOG#156. Superstatistics (I).

This post is the first of three dedicated to some of my followers. Those readers from Mexico (a nice country, despite the issues and particularities it has, as the one I live in…), ;). Why? Well, …Firstly, they have proved … Continue reading

LOG#154. Moonshine and 42: THE PAPER.

“(…) The answer to the Great Question…is…Forty-two(…)” said Deep Thought with infinity majesty and calm (frequently found quote from The Hitchhiker’s Guide to the Galaxy, Douglas Adams, London 1979) Dear readers, yesterday, while I was editing, re-editing and writing my … Continue reading

LOG#150. Bohr and Doctor Who: A=mc³.

The year 2013 is coming to its end…And I have a final gift for you. An impossible post! This year was the Bohr model 100th anniversary. I have talked about this subject already, here, here and here. The hydrogen spectrum is very important in … Continue reading

LOG#130. Finsler metrics.

“(…)A similar path to the same goal could also be taken in those manifolds in which the line element is expressed in a less simple way, e.g., by a fourth root of a differential expression of the fourth degree…(…)”                                                                                                                 … Continue reading