LOG#194. On minimons, maximons and darkons.

If you believe in both, relativity AND quantum mechanics, something that I presume you do due to experimental support, you are driven to admit that the speed of light is the maximal velocity (at least, the maximal 1-speed, in single … Continue reading

LOG#189. Fundamental challenges.

The marriage between gravity and quantum mechanics is “complicated”. The best physicists and brightest minds have tried, but only with partial success. String/superstring theory, now M-theory, is a curious story. The another story is canonical quantum gravity, or loop quantum … Continue reading

LOG#186. Polylogarithmic condensates.

Today, I return to my best friends. The polylogs! Are you ready for polylog wars? The polylogarithm can be represented by the next integral: (1)   As you know, if you follow my blog, you have         … Continue reading

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#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