# computation by recursion

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## 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 $\mathop{\mathrm{i}^{n}\mathrm{erfc}}\left(x\right)$. …
##### 2: 3.6 Linear Difference Equations
with $a_{n}\neq 0$, $\forall n$, can be computed recursively for $n=2,3,\dots$. … 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 $Y_{n}\left(1\right)$ is dominant and can be computed by forward recursion, whereas $J_{n}\left(1\right)$ 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 $E_{1}\left(z\right)$, $\mathrm{f}\left(z\right)$, and $\mathrm{g}\left(z\right)$ 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 $|\operatorname{ph}z|<\pi$ 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 $E_{p}\left(x\right)$ are described in Miller (1960) for $x>0$ and integer $p$. …
##### 9: 34.13 Methods of Computation
Methods of computation for $\mathit{3j}$ and $\mathit{6j}$ 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. …