Ramanujan developed a number of interesting closed-form expressions for generalized continued fractions. These include the almost integers 1/(1 + ) e^(-2 π)/(1 + ) e^(-4 π)/(1 + ...) | = | (sqrt((5 + sqrt(5))/2) - (sqrt(5) + 1)/2) e^(2π/5) | = | e^(2π/5)(sqrt(ϕsqrt(5)) - ϕ) | = | 0.998136... (OEIS A091667; Watson 1929, 1931; Hardy 1999, p.

continued fraction constants | generalized continued fraction | Rogers-Ramanujan continued fraction