Analytical site index solution for the generalized log-logistic height equation

Abstract

The generalized log-logistic height equation computes height as a function of age and a fixed base-age site index. This equation and its modifications have been used for many applications in various regions. It is seemingly apparent that this equation is analytically insolvable for the site index; no general analytical solution to this equation is readily available. This article presents such a solution that has proven to be valid and useful with all tested parameters. This solution is based on an adaptation of the Ramanujan's (1887-1920) solution for a trinomial with real-number exponents. Ramanujan's solution is a series that in many cases can be expressed as a closed-form equation. In the present context, this series may be used for derivations of various special cases of closed-form solutions, initial-condition difference and differential equations, and for various analytical sensitivity and trend analysis, as well as for efficient site index computations.