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Journal of Geodesy

, Volume 70, Issue 1–2, pp 110–116 | Cite as

A method for computing the coefficients in the product-sum formula of associated Legendre functions

  • Cheinway Hwang
Article

Abstract

The product of two associated Legendre functions can be represented by a finite series in associated Legendre functions with unique coefficients. In this study a method is proposed to compute the coefficients in this product-sum formula. The method is of recursive nature and is based on the straightforward polynomial form of the associated Legendre function's factor. The method is verified through the computation of integrals of products of two associated Legendre functions over a given interval and the computation of integrals of products of two Legendre polynomials over [0,1]. These coefficients are basically constant and can be used in any future related applications. A table containing the coefficients up to degree 5 is given for ready reference.

Keywords

Legendre Polynomial Legendre Function Polynomial Form Related Application Ready Reference 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1995

Authors and Affiliations

  • Cheinway Hwang
    • 1
  1. 1.Department of Civil EngineeringNational Chiao Tung UniversityHsinchuTaiwan

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