Astronomy and Astrophysics – Astrophysics
Scientific paper
May 1982
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1982ap%26ss..84...53s&link_type=abstract
Astrophysics and Space Science, vol. 84, no. 1, May 1982, p. 53-72. Research sponsored by the Science and Engineering Research
Astronomy and Astrophysics
Astrophysics
9
Elliptical Orbits, Orbital Mechanics, Series Expansion, Trigonometric Functions, Algorithms, Coefficients, Convergence, Proving, Recursive Functions, Tables (Data)
Scientific paper
Expansions of the functions H1, H2 and H3 are established both analytically and computationally for m positive integer, q real number, and Xi, epsilon which are both positive and less than unity. The treatment of each of these functions is divided into (1) the analytical developments for which the trigonometric series representation of the function and the literal analytical expressions of the coefficients will be given, (2) the computational developments of the coefficients, (3) a tabulation of the numerical results of the computational algorithms, and (4) proofs of the formulae.
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