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    Andrews-Schur Identity

    Definition

    The Andrews-Schur identity states sum_(k = 0)^n q^(k^2 + a k) [2n - k + a k]_q = sum_(k = - ∞)^∞ q^(10k^2 + (4a - 1) k) [2n + 2a + 2 n - 5k]_q [10k + 2a + 2]_q/[2n + 2a + 2]_q where [n m]_q is a q-binomial coefficient and [n]_q is a q-bracket. It is a polynomial identity for a = 0, 1 which implies the Rogers-Ramanujan identities by taking n->∞ and applying the Jacobi triple product identity.

    Related term

    Rogers-Ramanujan identities

    Associated person

    Friedrich Schur

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