Schur's determinants and partition theorems (Q1580545)

The formula \[ 1+ \sum^\infty_{n=1} {q^{n^2+ nn}\over (q; q)_n}= {(-1)^n q^{-{n\choose 2}} E_{n- 2}\over (q, q^4; q^5)_\infty}- {(-1)^n q^{-{n\choose 2}} D_{n-2}\over (q^2, q^3; q^5)_\infty}, \] which is a generalization of the Rogers-Ramanujan identities, is explained in the context of associated orthogonal polynomials and Schur's work on determinants. A further generalization is given, which contains many interesting special cases.