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VI—Formulæ and Scheme of Calculation for the Development of a Function of Two Variables in Spherical Harmonics

  • T. Bauschinger and C. G. Knott


When a function has been expressed as a series of spherical harmonics with constant coefficients, the determination of these coefficients from given values of the function is in the general case one of the most complicated operations which can be set before the calculator.

Since Gauss first carried out these operations in a calculation of this kind, efforts have not been wanting to simplify them and make their frequent application possible. The most successful of all in this respect was Franz Neumann, who showed that by a suitable choice of the argument the calculation could be materially shortened.



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page 63 note * Burckhardt, , Oszillierende Funktionen, pp. 384 ff.

page 63 note † Astronomische Nachrichten, Bd. xvi, p. 313 (1838).

page 63 note ‡ Sitzungsberichte der Konig. bayer. Akademie der Wissenschaften München: Math.-phys. Classe, Band xx, p. 499 (1891).

page 63 note § The part in square brackets has been added by the translator, so as to make the notations immediately intelligible to the reader.


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