Bilateral identities of the Rogers–Ramanujan type
Copyright policy )Bilateral identities of the Rogers–Ramanujan type
We derive by analytic means 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 multisums including multilateral extensions of the Andrews–Gordon identities, of the Andrews–Bressoud generalization of the Göllnitz–Gordon identities, of Bressoud’s even modulus identities, and other identities. Our closed form bilateral and multilateral summations appear to be the very first of their kind.
- University of Vienna Austria
bilateral summations, \(q\)-series, q-Series, q-series, multilateral summations, 11P84 (Primary) 33D15 (Secondary), 101025 Number theory, Partition identities; identities of Rogers-Ramanujan type, Basic hypergeometric functions in one variable, \({}_r\phi_s\), Andrews-Gordon type identities, FOS: Mathematics, Mathematics - Combinatorics, Bilateral summations, Number Theory (math.NT), 101025 Zahlentheorie, Mathematics - Number Theory, Rogers–Ramanujan type identities, basic hypergeometric series, Basic hypergeometric series, Multilateral summations, Rogers-Ramanujan type identities, Combinatorics (math.CO)
bilateral summations, \(q\)-series, q-Series, q-series, multilateral summations, 11P84 (Primary) 33D15 (Secondary), 101025 Number theory, Partition identities; identities of Rogers-Ramanujan type, Basic hypergeometric functions in one variable, \({}_r\phi_s\), Andrews-Gordon type identities, FOS: Mathematics, Mathematics - Combinatorics, Bilateral summations, Number Theory (math.NT), 101025 Zahlentheorie, Mathematics - Number Theory, Rogers–Ramanujan type identities, basic hypergeometric series, Basic hypergeometric series, Multilateral summations, Rogers-Ramanujan type identities, Combinatorics (math.CO)
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