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1: 27.17 Other Applications
Reed et al. (1990, pp. 458–470) describes a number-theoretic approach to Fourier analysis (called the arithmetic Fourier transform) that uses the Möbius inversion (27.5.7) to increase efficiency in computing coefficients of Fourier series. …
2: 29.20 Methods of Computation
Subsequently, formulas typified by (29.6.4) can be applied to compute the coefficients of the Fourier expansions of the corresponding Lamé functions by backward recursion followed by application of formulas typified by (29.6.5) and (29.6.6) to achieve normalization; compare §3.6. …
§29.20(ii) Lamé Polynomials
3: Bibliography S
  • K. Schulten and R. G. Gordon (1976) Recursive evaluation of 3 j - and 6 j - coefficients. Comput. Phys. Comm. 11 (2), pp. 269–278.
  • K. Srinivasa Rao, V. Rajeswari, and C. B. Chiu (1989) A new Fortran program for the 9 - j angular momentum coefficient. Comput. Phys. Comm. 56 (2), pp. 231–248.
  • K. Srinivasa Rao and K. Venkatesh (1978) New Fortran programs for angular momentum coefficients. Comput. Phys. Comm. 15 (3-4), pp. 227–235.
  • K. Srinivasa Rao (1981) Computation of angular momentum coefficients using sets of generalized hypergeometric functions. Comput. Phys. Comm. 22 (2-3), pp. 297–302.
  • A. J. Stone and C. P. Wood (1980) Root-rational-fraction package for exact calculation of vector-coupling coefficients. Comput. Phys. Comm. 21 (2), pp. 195–205.
  • 4: 3.11 Approximation Techniques
    If we have a sufficiently close approximation …to f ( x ) , then the coefficients a k can be computed iteratively. …
    Calculation of Chebyshev Coefficients
    Any five approximants arranged in the Padé table as …
    5: 6.20 Approximations
  • Luke (1969b, p. 25) gives a Chebyshev expansion near infinity for the confluent hypergeometric U -function (§13.2(i)) from which Chebyshev expansions near infinity for E 1 ( z ) , f ( z ) , and g ( z ) follow by using (6.11.2) and (6.11.3). Luke also includes a recursion scheme for computing the coefficients in the expansions of the U functions. If | ph z | < π the scheme can be used in backward direction.

  • 6: Bibliography T
  • T. Tamura (1970) Angular momentum coupling coefficients. Comput. Phys. Comm. 1 (5), pp. 337–342.
  • 7: Bibliography F
  • D. F. Fang and J. F. Shriner (1992) A computer program for the calculation of angular-momentum coupling coefficients. Comput. Phys. Comm. 70 (1), pp. 147–153.
  • 8: 30.16 Methods of Computation
    The coefficients a n , r m ( γ 2 ) are computed as the recessive solution of (30.8.4) (§3.6), and normalized via (30.8.5). … The coefficients a n , k m ( γ 2 ) calculated in §30.16(ii) can be used to compute S n m ( j ) ( z , γ ) , j = 1 , 2 , 3 , 4 from (30.11.3) as well as the connection coefficients K n m ( γ ) from (30.11.10) and (30.11.11). …
    9: Bibliography K
  • T. A. Kaeding (1995) Pascal program for generating tables of SU ( 3 ) Clebsch-Gordan coefficients. Comput. Phys. Comm. 85 (1), pp. 82–88.
  • 10: Bibliography E
  • D. Erricolo (2006) Algorithm 861: Fortran 90 subroutines for computing the expansion coefficients of Mathieu functions using Blanch’s algorithm. ACM Trans. Math. Software 32 (4), pp. 622–634.