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11: Bibliography B
  • A. Bar-Shalom and M. Klapisch (1988) NJGRAF: An efficient program for calculation of general recoupling coefficients by graphical analysis, compatible with NJSYM. Comput. Phys. Comm. 50 (3), pp. 375–393.
  • W. G. C. Boyd (1990a) Asymptotic Expansions for the Coefficient Functions Associated with Linear Second-order Differential Equations: The Simple Pole Case. In Asymptotic and Computational Analysis (Winnipeg, MB, 1989), R. Wong (Ed.), Lecture Notes in Pure and Applied Mathematics, Vol. 124, pp. 53–73.
  • P. G. Burke (1970) A program to calculate a general recoupling coefficient. Comput. Phys. Comm. 1 (4), pp. 241–250.
  • 12: Bibliography Z
  • H. S. Zuckerman (1939) The computation of the smaller coefficients of J ( τ ) . Bull. Amer. Math. Soc. 45 (12), pp. 917–919.
  • 13: Bibliography D
  • R. McD. Dodds and G. Wiechers (1972) Vector coupling coefficients as products of prime factors. Comput. Phys. Comm. 4 (2), pp. 268–274.
  • O. Dragoun and G. Heuser (1971) A program to calculate internal conversion coefficients for all atomic shells without screening. Comput. Phys. Comm. 2 (7), pp. 427–432.
  • 14: 11.6 Asymptotic Expansions
    These and higher coefficients c k ( λ ) can be computed via the representations in Nemes (2015b). …
    15: 31.18 Methods of Computation
    §31.18 Methods of Computation
    Independent solutions of (31.2.1) can be computed in the neighborhoods of singularities from their Fuchs–Frobenius expansions (§31.3), and elsewhere by numerical integration of (31.2.1). Subsequently, the coefficients in the necessary connection formulas can be calculated numerically by matching the values of solutions and their derivatives at suitably chosen values of z ; see Laĭ (1994) and Lay et al. (1998). …The computation of the accessory parameter for the Heun functions is carried out via the continued-fraction equations (31.4.2) and (31.11.13) in the same way as for the Mathieu, Lamé, and spheroidal wave functions in Chapters 2830.
    16: 9.19 Approximations
  • Corless et al. (1992) describe a method of approximation based on subdividing into a triangular mesh, with values of Ai ( z ) , Ai ( z ) stored at the nodes. Ai ( z ) and Ai ( z ) are then computed from Taylor-series expansions centered at one of the nearest nodes. The Taylor coefficients are generated by recursion, starting from the stored values of Ai ( z ) , Ai ( z ) at the node. Similarly for Bi ( z ) , Bi ( z ) .

  • 17: Bibliography M
  • A. P. Magnus (1995) Painlevé-type differential equations for the recurrence coefficients of semi-classical orthogonal polynomials. J. Comput. Appl. Math. 57 (1-2), pp. 215–237.
  • 18: Bibliography
  • H. Appel (1968) Numerical Tables for Angular Correlation Computations in α -, β - and γ -Spectroscopy: 3 j -, 6 j -, 9 j -Symbols, F- and Γ -Coefficients. Landolt-Börnstein Numerical Data and Functional Relationships in Science and Technology, Springer-Verlag.
  • 19: 10.74 Methods of Computation
    §10.74 Methods of Computation
    §10.74(vi) Zeros and Associated Values
    Hankel Transform
    20: Bibliography V
  • H. Van de Vel (1969) On the series expansion method for computing incomplete elliptic integrals of the first and second kinds. Math. Comp. 23 (105), pp. 61–69.
  • J. Van Deun and R. Cools (2008) Integrating products of Bessel functions with an additional exponential or rational factor. Comput. Phys. Comm. 178 (8), pp. 578–590.
  • C. Van Loan (1992) Computational Frameworks for the Fast Fourier Transform. Frontiers in Applied Mathematics, Vol. 10, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA.
  • A. van Wijngaarden (1953) On the coefficients of the modular invariant J ( τ ) . Nederl. Akad. Wetensch. Proc. Ser. A. 56 = Indagationes Math. 15 56, pp. 389–400.
  • M. N. Vrahatis, T. N. Grapsa, O. Ragos, and F. A. Zafiropoulos (1997a) On the localization and computation of zeros of Bessel functions. Z. Angew. Math. Mech. 77 (6), pp. 467–475.