About the Project
NIST

computation by recursion

AdvancedHelp

(0.001 seconds)

1—10 of 19 matching pages

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: 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). …
    10: 12.18 Methods of Computation
    §12.18 Methods of Computation
    Because PCFs are special cases of confluent hypergeometric functions, the methods of computation described in §13.29 are applicable to PCFs. These include the use of power-series expansions, recursion, integral representations, differential equations, asymptotic expansions, and expansions in series of Bessel functions. …