LOG#166. D-dimensional laws(I).

My next thread of nested articles are aimed to explore (shallowly, only) the issue of extra dimensions (of space and time!). Let me begin with the Gauss law for the electric field. The electrical flux in D-dimensional space reads, for … 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