Computer Science – Numerical Analysis
Scientific paper
Jul 1976
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1976ap%26ss..42..425l&link_type=abstract
Astrophysics and Space Science, vol. 42, July 1976, p. 425-440.
Computer Science
Numerical Analysis
6
Circular Orbits, Eclipsing Binary Stars, Light Curve, Stellar Luminosity, Hypergeometric Functions, Numerical Analysis, Partial Differential Equations, Power Series
Scientific paper
This paper discusses a method for improving on the numerical evaluation of the light changes exhibited by a distorted eclipsing binary system. In the theory formulated by Kopal (1959), certain boundary integrals due to the distortion of both components have been calculated in terms of the Appell hypergeometric series of the first kind. The values of the four parameters appearing in these series differ according to whether one is dealing with a partial or an annular eclipse. To accelerate the numerical evaluation of the light changes one should avoid recomputing such infinite series for continuous values of the parameters. This can be achieved by making use of certain recursion formulae which hold for the foregoing series. We have provided here a procedure that yields 48 recursion formulae for the Appell hypergeometric series and have specifically calculated four new independent recursion formulae relevant to the astrophysical problem.
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