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Analytical Site Index Solution for the Generalized Log-Logistic Height Equation

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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. For. Sci. 46(2):291-296

Keywords: Analytical solutions; base-age invariant; convergent series; numerical solutions; polynomial solutions; site index models

Document Type: Journal Article

Publication date: 2000-05-01

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  • Forest Science is a peer-reviewed journal publishing fundamental and applied research that explores all aspects of natural and social sciences as they apply to the function and management of the forested ecosystems of the world. Topics include silviculture, forest management, biometrics, economics, entomology & pathology, fire & fuels management, forest ecology, genetics & tree improvement, geospatial technologies, harvesting & utilization, landscape ecology, operations research, forest policy, physiology, recreation, social sciences, soils & hydrology, and wildlife management.
    Forest Science is published bimonthly in February, April, June, August, October, and December.

    2015 Impact Factor: 1.702
    Ranking: 16 of 66 in forestry

    Also published by SAF:
    Journal of Forestry
    Other SAF Publications
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