Ramanujan χ-function | Ramanujan f-function | Ramanujan ψ-function

Ramanujan's two-variable theta function f(a, b) is defined by f(a, b) congruent sum_(n = - ∞)^∞ a^(n(n + 1)/2) b^(n(n - 1)/2) for left bracketing bar a b right bracketing bar <1 (Berndt 1985, p. 34; Berndt et al. 2000). It satisfies f(-1, a) = 0 and f(a, b) | = | f(b, a) | = | (-a;a b)_∞ (-b;a b)_∞ (a b;a b)_∞ (Berndt 1985, pp. 34-35; Berndt et al. 2000), where (a;q)_k is a q-Pochhammer symbol, i.e., a q-series.

Jacobi triple product | pentagonal number theorem | q-series | q-series identities | Ramanujan ϕ-function | Rogers-Ramanujan continued fraction | Schröter's formula