Title: How to discover the Rogers-Ramanujan identities
Speaker: Gaurav Bhatnagar, SPS, JNU
Where: Seminar Room, School of Physical Sciences (SPS)
Speaker: Gaurav Bhatnagar, SPS, JNU
Where: Seminar Room, School of Physical Sciences (SPS)
Abstract:
The Rogers-Ramanujan identities were sent by Ramanujan to Hardy in a letter more than a 100 years ago. In the next few years, the identities were circulated among mathematicians, but nobody, including Ramanujan, could prove them. Then one day, while riffling through old back copies of the journal, Ramanujan discovered them in an obscure paper written in 1894 by the English mathematician Rogers. Later, these identities were discovered independently by Schur in a combinatorial context, and then again in 1980 by Baxter in the context of mathematical physics. We don’t know how Ramanujan got to them, but we examine a method to conjecture these identities which Askey has suggested may be the way Ramanujan discovered them.
The Rogers-Ramanujan identities were sent by Ramanujan to Hardy in a letter more than a 100 years ago. In the next few years, the identities were circulated among mathematicians, but nobody, including Ramanujan, could prove them. Then one day, while riffling through old back copies of the journal, Ramanujan discovered them in an obscure paper written in 1894 by the English mathematician Rogers. Later, these identities were discovered independently by Schur in a combinatorial context, and then again in 1980 by Baxter in the context of mathematical physics. We don’t know how Ramanujan got to them, but we examine a method to conjecture these identities which Askey has suggested may be the way Ramanujan discovered them.
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