Abstract
Recurrence relations for the evaluation of the integrals of associated Legendre functions over an arbitrary interval within (0°, 90°) have been derived which yield sufficiently accurate results throughout the entire range of their possible applications. These recurrence relations have been used to compute integrals up to degree 100 and similar computations can be carried out without any difficulty up to a degree as high as the memory in a computer permits. The computed values have been tested with independent check formulae, also derived in this work; the corresponding relative errors never exceed 10−23 in magnitude.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
D.C. CHRISTODOULIDIS and K.E. KATSAMBALOS: An Analysis on the Precision in the Computation of the Integrals of the Fully Normalized Associated Legendre Functions, Report of Dept. Geod. Sci., Ohio State Univ., U.S.A., 1977.
W.A. HEISKANEN, and H. MORITZ: Physical Geodesy, W.H. Freeman, and Co., San Francisco, 1967.
E.W. HOBSON: The Theory of Spherical and Ellipsoidal Harmonics, Cambridge Univ. Press, U.K., 1955.
D. NAGY: High Degree Spherical Harmonic Expansion of Gravity Data, EOS Trans. AGU, Vol, 58, p. 987, 1977.
R.G.E. YOUNG: Combining Satellite Altimetry and Surface Gravimetry in Geodetic Determinations, TE-37, Massachusetts Institute of Technology, Measurement System Lab., 1970.
Author information
Authors and Affiliations
Additional information
Contribution from the Earth Physics Branch No. 719
Rights and permissions
About this article
Cite this article
Paul, M.K. Recurrence relations for integrals of Associated Legendre functions. Bull. Geodesique 52, 177–190 (1978). https://doi.org/10.1007/BF02521771
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF02521771