Continued Fraction Evaluation of the Universal Y’s Functions

Affiliation(s)

^{1}
Department of Astronomy, Faculty of Science, King Abdulaziz University, Jeddah, KSA.

^{2}
Department of Astronomy, National Research Institute of Astronomy and Geophysics, Cairo, Egypt.

^{3}
Department of Mathematics, Preparatory Year, Qassim University, Buraidah, KSA.

^{4}
Department of Mathematics, Preparatory Year for Girls Branch, Hail University, Hail, KSA.

ABSTRACT

In the present paper, an efficient algorithm based on the continued fractions theory was established for the universal Y’s functions of space dynamics. The algorithm is valid for any conic motion (elliptic, parabolic or hyperbolic).

In the present paper, an efficient algorithm based on the continued fractions theory was established for the universal Y’s functions of space dynamics. The algorithm is valid for any conic motion (elliptic, parabolic or hyperbolic).

Cite this paper

Sharaf, M. , Saad, A. , Motelp, N. (2015) Continued Fraction Evaluation of the Universal Y’s Functions.*International Journal of Astronomy and Astrophysics*, **5**, 15-19. doi: 10.4236/ijaa.2015.51003.

Sharaf, M. , Saad, A. , Motelp, N. (2015) Continued Fraction Evaluation of the Universal Y’s Functions.

References

[1] Sharaf, M.A. and Saad, A.S. (2014) New Set of Universal Functions for the Two Body-Initial Value Problem. Astrophysics and Space Science, 349, 71-81. (Paper I)

[2] Gautschi, W. (1967) Computational Aspects of Three-Term Recurrence Relations. SIAM Review, 9, 24-82.

http://dx.doi.org/10.1137/1009002

[3] Sharaf, M.A. (2006) Computations of the Cosmic Distance Equation. Applied Mathematics and Computation, 174, 1269-1278.

http://dx.doi.org/10.1016/j.amc.2005.05.054

[4] Sharaf, M.A., Almleaky, Y.M., Malawi, A.A., Goharji, A.A. and Basurah, H.M. (2004) Symbolic Analytical Expressions of the Physical Characteristics for N-Dimensional Radially Symmetrical Isothermal Models. AJSE, King Fahd, Univ., 29, 67-82.

[5] Sharaf, M.A. and Banajh, M.A. (2001) Continued Fraction Evaluation of the Stumpff Functions of Space Dynamics. Scientific Journal of Faculty of Science, Minufiya University, XV, 267-282.

[6] Sharaf, M.A. and Najmuldeen, S.A. (2001) Continued Fraction Evaluation of the Normal Distribution Function. Scientific Journal of Faculty of Science, Minufiya University, XV, 311-324.

[7] Battin, R.H. (1999) An Introduction to the Mathematics and Methods of Astrodynamics. Revised Edition, AIAA, Education Series, Reston, Virginia.

[1] Sharaf, M.A. and Saad, A.S. (2014) New Set of Universal Functions for the Two Body-Initial Value Problem. Astrophysics and Space Science, 349, 71-81. (Paper I)

[2] Gautschi, W. (1967) Computational Aspects of Three-Term Recurrence Relations. SIAM Review, 9, 24-82.

http://dx.doi.org/10.1137/1009002

[3] Sharaf, M.A. (2006) Computations of the Cosmic Distance Equation. Applied Mathematics and Computation, 174, 1269-1278.

http://dx.doi.org/10.1016/j.amc.2005.05.054

[4] Sharaf, M.A., Almleaky, Y.M., Malawi, A.A., Goharji, A.A. and Basurah, H.M. (2004) Symbolic Analytical Expressions of the Physical Characteristics for N-Dimensional Radially Symmetrical Isothermal Models. AJSE, King Fahd, Univ., 29, 67-82.

[5] Sharaf, M.A. and Banajh, M.A. (2001) Continued Fraction Evaluation of the Stumpff Functions of Space Dynamics. Scientific Journal of Faculty of Science, Minufiya University, XV, 267-282.

[6] Sharaf, M.A. and Najmuldeen, S.A. (2001) Continued Fraction Evaluation of the Normal Distribution Function. Scientific Journal of Faculty of Science, Minufiya University, XV, 311-324.

[7] Battin, R.H. (1999) An Introduction to the Mathematics and Methods of Astrodynamics. Revised Edition, AIAA, Education Series, Reston, Virginia.