Explicit solution of the Kepler equation

Physics of Particles and Nuclei Letters

Volumn 4, Issue 3, 2007, Pages 213-216

  Dubinov, A E ^a   Galidakis, I N ^b  

^a RUSSIAN FEDERAL NUCLEAR CENTER VNIIEF   (Russian Federation)

^b UNIVERSITY OF CRETE   (Greece)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 34250183859     PISSN: 15474771     EISSN: None     Source Type: Journal    
DOI: 10.1134/S1547477107030028     Document Type: Article

References (15)

1. P. Colwell, Solving Kepler's Equation over Three Centuries (Willmann-Bell Inc., Richmond, 1993).
2. G. N. Duboshin, Celestial Mechanics. Basic Problems and Methods (Nauka, Moscow, 1968) [in Russian].
3. E. P. Aksenov, Special Functions in Celestial Mechanics (Nauka, Moscow, 1986) [in Russian].
4. C. E. Siewert and E. E. Burniston, "An Exact Analytical Solution of Kepler's Equation," Celestial Mechanics 6, 294 (1972).
5. I. A. Shelaev, " Kepler's Equation Solution, " Preprint OIYaI R2-2002-298 (Dubna, 2002).
6. M. Palacios, "Improving the Solution of Kepler's Equation and Related Problems," Monografias del Sem. Mat. "Garcia de Galdeano" 21, 145-157 (2001).
7. R. M. Corless et al., "On the Lambert W Function," Adv. Comp. Math. 5, 329-359 (1996).
8. A. E. Dubinov, I. D. Dubinova, and S. K. Saikov, W -Function of Lambert: Table of Integrals and Other Mathematical Properties (SarFTI, Sarov, 2004) [in Russian].
9. I. N. Galidakis, "An Infinite Family of Lambert W -Like Functions and Their Use in Numerically Solving Exponential Tower Equations," http://users.forthnet.gr/ath/igal/math/LWExtension.html.
10. I. N. Galidakis, "On Solving the p -th Complex Auxiliary Equation f (p) (z) = z, " Complex Variables 50 (13), 977-997 (2005).
11. F. D. Parker, "Integrals of Inverse Functions," Am. Math. Month. 62 (6), 439-440 (1955).
12. S. Saks and A. Sygmund, Analytical Functions (Hafner Publ. Comp., New York, 1952).
13. B. Salvy, "Fast Computation of Some Asymptotic Functional Inverses," J. Symbolic Computation 17, 227-236 (1999).
14. B. Salvy and J. Shackell, "Symbolic Asymptotics: Multiseries of Inverse Functions," J. Symbolic Computation 27, 543-563 (1999).
15. S. D. Skorokhodov, "Pade's Approximations and Numerical Analysis of Ryman's dzeta-Function," Zh. Vychisl. Mat. Mat. Fiz. 43 (9), 1330-1352 (2003) [Com. Math. 43, 1277-1298 (2003)].