Michael J. Schlosser
Bilateral identities of the Rogers-Ramanujan type
We derive by analytic means a number of bilateral identities of the
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.
Given that the classical Rogers-Ramanujan identities have well-established
connections to various areas in mathematics and in physics, it is natural
to expect that the new bilateral and multilateral identities can be similarly
connected to those areas. This is supported by concrete
combinatorial interpretations for a collection of four bilateral
companions to the classical Rogers-Ramanujan identities.
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