A Taylor series expansion for Lotka's r

A. J. Latka and F. R. Sharpe published their classical deterministic population model in 1911, and since that date, numerous numerical methods have been suggested for solving the integral equation inherent in the model. We consider the familiar integral equation (Equation (1)) and derive a Taylor series for ro, the unique real solution. The series is no more advantageous from the calculation point of view than many previous solutions, but it may be useful in a theoretical context. The effects on the intrinsic rate of increase of the population due to changes in the cumulants of the net maternity function are readily discernible.