LOG#178. Divergent sums: The Number awakens!

Are you divergent? Divergences are usually sums or results you would consider “infinite” or “ill-defined” (unexistent) in normal terms. But don’t be afraid. You can learn to “regularize” a divergent series or sum. Really? Oh, yes!Beyond faction of a well-known … Continue reading

LOG#170. The shortest papers ever: the list.

Hi, everyone. In this short post I am going to discuss some of the shortest papers ever written all over the world!!!!! This idea came to my mind due to a post by @seanmcarroll on twitter and other social networks… … Continue reading

LOG#168. D-dimensional laws(III).

The question of the origin of mass is one of the more important issues in theoretical physics. The existence (or not) of extra dimensions of space and time will likely affect to the final solution of this unsolved problem. The … Continue reading

LOG#165. Rogers-Ramanujan identities.

There are some cool identities, very well known to mathematicians and some theoretical physicists or chemists, related with Ramanujan. They are commonly referred as Rogers-Ramanujan identities (Rogers, 1894; Ramanujan 1913,1917 and Rogers and Ramanujan, 1919). They are related to some … Continue reading

LOG#164. Theta functions.

Hi, there! We are going to explore more mathematical objects in this post. Today, the objects to study are theta functions. A prototype is the Jacobi theta function: (1)   where and . It satisfies the functional equation (2)   … Continue reading

LOG#163. Q-stuff and wonderful functions.

In this blog post I am going to define and talk about some interesting objects. They are commonly referred as q-objects in general. The q-Pochhammer symbol is the next product: (1)   with . The infinite product extension is also … Continue reading

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