(1) $ \left(\frac{Y}{L}\right) = \left(\frac{K}{Y}\right)^\left(\frac{\alpha}{1-\alpha}\right)E $ :: production function
(2) $ \left(\frac{Y}{L}\right)^{*} = \left(\frac{s}{n+g+\delta}\right)^ \left(\frac{\alpha}{1-\alpha}\right)E $ :: equilibrium balanced-growth path
(3) $ \frac{d\left(\frac{K}{Y}\right)}{dt} = -(1-\alpha)(n+g+\delta)\left(\frac{K}{Y} - \frac{s}{n+g+\delta}\right)$ :: convergence differential equation
(4) $ \frac{K_t}{Y_t} = \frac{s}{n+g+\delta} + \left(\frac{K}{Y} - \frac{s}{n+g+\delta}\right) e^{-(1-\alpha)(n+g+\delta)t} $
The most useful form of the production function:
(1) $ \left(\frac{Y}{L}\right) = \left(\frac{K}{Y}\right)^\left(\frac{\alpha}{1-\alpha}\right)E $
The most useful form of equilibrium:
(2) $ \left(\frac{Y}{L}\right)^{*} = \left(\frac{s}{n+g+\delta}\right)^ \left(\frac{\alpha}{1-\alpha}\right)E $
(3) $ \frac{d\left(\frac{K}{Y}\right)}{dt} = -(1-\alpha)(n+g+\delta)\left(\frac{K}{Y} - \frac{s}{n+g+\delta}\right)$
(4) $ \frac{K_t}{Y_t} = \frac{s}{n+g+\delta} + \left(\frac{K}{Y} - \frac{s}{n+g+\delta}\right) e^{-(1-\alpha)(n+g+\delta)t} $
(5) $ \left(\frac{Y}{L}\right) = \left(\frac{K}{L}\right)^{\alpha}(E)^{1-\alpha} $
(6) $ \frac{1}{L}\frac{dL}{dt} = n $
(7) $ \frac{1}{E}\frac{dE}{dt} = g $
(8) $ \frac{1}{K}\frac{dLK}{dt} = s\left(\frac{Y}{K}\right) - \delta $