Open AccessV. On the integrals of the squares of ellipsoidal surface harmonic functions
Author(s) -
George Howard Darwin
Publication year - 1904
Publication title -
philosophical transactions of the royal society of london series a containing papers of a mathematical or physical character
Language(s) - English
Resource type - Journals
eISSN - 2053-9258
pISSN - 0264-3952
DOI - 10.1098/rsta.1904.0017
Subject(s) - ellipsoid , harmonics , surface (topology) , harmonic , series (stratigraphy) , stability (learning theory) , mathematics , mathematical analysis , spherical harmonics , harmonic analysis , pear , calculus (dental) , physics , geometry , computer science , quantum mechanics , geology , medicine , paleontology , dentistry , astronomy , voltage , machine learning , world wide web
This paper forms a sequel to three others published in Series A of the. ‘ Philosophical Transactions,’ namely, “ On Ellipsoidal Harmonic Analysis,” vol. 197, pp. 461-557, “ On the Pear-shaped Figure of Equilibrium of a Rotating Mass of Liquid,” vol. 198, pp. 301-381, and “ On the Stability of the Pear-shaped Figure of Equilibrium, &c.,” vol. 200, pp. 251-314. 1 shall refer to these three papers as “ Harmonics,” “ The Pear-shaped Figure,” and “ Stability.” In “ Harmonics,” the functions being expressed approximately, approximate formulae are found for the integrals over the surface of the ellipsoid of the squares of all the surface harmonics. These integrals are of course required whenever it is proposed to make practical use of this method of analysis, and the evaluation of them is therefore an absolutely essential step towards any applications.
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