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computation by recursion

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1: 7.22 Methods of Computation
The recursion scheme given by (7.18.1) and (7.18.7) can be used for computing i n erfc ( x ) . …
2: 3.6 Linear Difference Equations
with a n 0 , n , can be computed recursively for n = 2 , 3 , . … A “trial solution” is then computed by backward recursion, in the course of which the original components of the unwanted solution g n die away. … Then computation of w n by forward recursion is unstable. …
Example 1. Bessel Functions
Thus Y n ( 1 ) is dominant and can be computed by forward recursion, whereas J n ( 1 ) is recessive and has to be computed by backward recursion. …
3: Bibliography W
  • M. E. Wojcicki (1961) Algorithm 44: Bessel functions computed recursively. Comm. ACM 4 (4), pp. 177–178.
  • 4: 3.9 Acceleration of Convergence
    The ratio of the Hankel determinants in (3.9.9) can be computed recursively by Wynn’s epsilon algorithm: …
    5: Bibliography G
  • W. Gautschi (1961) Recursive computation of the repeated integrals of the error function. Math. Comp. 15 (75), pp. 227–232.
  • A. Gil, J. Segura, and N. M. Temme (2006c) The ABC of hyper recursions. J. Comput. Appl. Math. 190 (1-2), pp. 270–286.
  • 6: 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.

  • 7: 3.11 Approximation Techniques
    For the recursive computation of [ n + k / k ] f by Wynn’s epsilon algorithm, see (3.9.11) and the subsequent text. …
    8: 8.25 Methods of Computation
    Stable recursive schemes for the computation of E p ( x ) are described in Miller (1960) for x > 0 and integer p . …
    9: 18.40 Methods of Computation
    A simple set of choices is spelled out in Gordon (1968) which gives a numerically stable algorithm for direct computation of the recursion coefficients in terms of the moments, followed by construction of the J-matrix and quadrature weights and abscissas, and we will follow this approach: Let N be a positive integer and define …
    10: 34.13 Methods of Computation
    Methods of computation for 3 j and 6 j symbols include recursion relations, see Schulten and Gordon (1975a), Luscombe and Luban (1998), and Edmonds (1974, pp. 42–45, 48–51, 97–99); summation of single-sum expressions for these symbols, see Varshalovich et al. (1988, §§8.2.6, 9.2.1) and Fang and Shriner (1992); evaluation of the generalized hypergeometric functions of unit argument that represent these symbols, see Srinivasa Rao and Venkatesh (1978) and Srinivasa Rao (1981). …