科学研究
报告题目:

Bilateral identities of the Rogers-Ramanujan type

报告人:

Michael J. Schlosser 副教授(University of Vienna)

报告时间:

报告地点:

公司雷军科技楼601报告厅

报告摘要:

The classical Rogers-Ramanujan identities have intrigued many mathematicians around the world for more than a century. MacMahon and Schur have independently proposed combinatorial interpretations for these identities, and meanwhile connections to various other areas in mathematics and in physics have been revealed, in particular to Lie theory, statistical mechanics, conformal field theory, proabability theory and knot theory. In addition to the Rogers-Ramanujan identities there are numerous identities of similar type, as well as multisum versions.

By taking suitable limits in identities for bilateral basic hypergeometric series, we are able to derive a number of bilateral identities of the Rogers-Ramanujan type.

Our results include bilateral extensions of the Rogers-Ramanujan and the Göllnitz-Gordon identities, and of related identities by Ramanujan, Jackson, and Slater.

We give corresponding results for multiseries including multilateral extensions of the Andrews-Gordon identities, of Bressoud's even modulus identities, and other identities. The here revealed closed form bilateral and multilateral summations appear to be the very first of their kind.