On the J-integrals associated with close binary systems - New recursion formulae

Mathematics

Scientific paper

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Binary Stars, Entire Functions, Numerical Integration, Recursive Functions, Stellar Radiation, Light Emission, Partial Differential Equations, Series (Mathematics), Stellar Models

Scientific paper

J-integrals were introduced by Kopal (1959) for the numerical evaluation of the light changes exhibited by tidally and rotationally distorted eclipsing binary systems. The present paper enumerates all recursion formulas for the J-integrals of a partial eclipse. Recursion formulas are obtained first for the Appell hypergeometric series of the first kind, and a relation existing between this series and the J-integrals is then used to derive recursion formulas entailing variation of all three indices of the J-integrals. It is noted that some of these formulas generalize Kopal's results valid for zero values of the m or gamma index.

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