Slater's identity

The Jackson-Slater identity is the q-series identity of Rogers-Ramanujan-type given by sum_(k = 0)^∞ q^(2k^2)/(q)_(2k) | = | ((q, q^7, q^8 ;q^8)_∞ (q^6, q^10 ;q^16)_∞)/(q)_∞ | = | (f(q^3, q^5))/(f(-q^2)) | = | 1 + q^2 + q^3 + 2q^4 + 2q^5 + 3q^6 + 3q^6 + 5q^7 + ... (OEIS A069910), where (a^i, b^j, ..., a^p ;q)_∞ is extended q-series notation and f(a, b) is a Ramanujan theta function.

q-series | Rogers-Ramanujan identities