## Andrews-Schur Identity

 (1)
where is a Gaussian Polynomial. It is a Polynomial identity for , 1 which implies the Rogers-Ramanujan Identities by taking and applying the Jacobi Triple Product identity. A variant of this equation is

 (2)
where the symbol in the Sum limits is the Floor Function (Paule 1994). The Reciprocal of the identity is

 (3)

for , 1 (Paule 1994). For , (1) and (2) become

 (4)

References

Andrews, G. E. A Polynomial Identity which Implies the Rogers-Ramanujan Identities.'' Scripta Math. 28, 297-305, 1970.

Paule, P. Short and Easy Computer Proofs of the Rogers-Ramanujan Identities and of Identities of Similar Type.'' Electronic J. Combinatorics 1, R10 1-9, 1994. http://www.combinatorics.org/Volume_1/volume1.html#R10.