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 objects called basic hypergeometric functions, some q-analogues of the classical hypergeometric functions that some people study in calculus and the theory of special functions. We write them as follows:
and where . It shows that and are modular functions of . These identities arise in some places of superstring theory, and in the hard hexagon model of statistical mechanics. Moreover, they are the key ingredients to derive the Ramanujan’s continued fraction
that were some of the most remarkable findings that Ramanujan sent to the English mathematician Hardy in the United Kingdom at the first of the 20th century…
May Ramanujan be with you!
Hi, this is Li from China. I am a postgraduate student. What I wanna say is that your blog is AWESOME! And I look forward to enjoying your first blog in 2018 : D
Firstly: Many thanks for your comment and your encouragement! I am alone with this blog and I had (yet have) health issues and other problems that are delaying my further posts. I don’t know how long I am going to last into further posts. Some of them are already written long ago, but without stable job (I had not stable job until now, not my dream, but I can pay the bills…), my fears concerning my weak health in the last years have complicated the stuff. The post 200 is…very special and it will be long (indeed, I would like to publish before but I don’t know how) since I have always made a special post every 50 posts. I know there are eager readers, but I am alone and with no support to do this in good conditions (I mean, free time).
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