recursion relations

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1: 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). …

2: 34.7 Basic Properties: $\mathit{9j}$ Symbol

… ►

§34.7(iii) Recursion Relations

►For recursion relations see Varshalovich et al. (1988, §10.5). …

3: 34.5 Basic Properties: $\mathit{6j}$ Symbol

… ►

§34.5(iii) Recursion Relations

… ►For further recursion relations see Varshalovich et al. (1988, §9.6) and Edmonds (1974, pp. 98–99). …

4: 34.3 Basic Properties: $\mathit{3j}$ Symbol

… ►

§34.3(iii) Recursion Relations

… ►For these and other recursion relations see Varshalovich et al. (1988, §8.6). …

5: 18.30 Associated OP’s

… ►The recursion relation for the associated Laguerre polynomials, see (18.30.2), (18.30.3) is … ►The recursion relation for the associated Hermite polynomials, see (18.30.2), and (18.30.3), is … ►Defining associated orthogonal polynomials and their relationship to their corecursive counterparts is particularly simple via use of the recursion relations for the monic, rather than via those for the traditional polynomials. …

6: 18.40 Methods of Computation

… ►See Gautschi (1983) for examples of numerically stable and unstable use of the above recursion relations, and how one can then usefully differentiate between numerical results of low and high precision, as produced thereby. …

7: Bibliography L

… ►

J. D. Louck (1958) New recursion relation for the Clebsch-Gordan coefficients. Phys. Rev. (2) 110 (4), pp. 815–816.

ⓘ

External Links:: Document, MathReview, ZentralBlatt
Referenced by:: §34.3(iii).
Encodings:: BibTeX

…

8: Bibliography M

… ►

M. Micu (1968) Recursion relations for the

3

j

symbols. Nuclear Physics A 113 (1), pp. 215–220.

ⓘ

External Links:: Document
Referenced by:: §34.3(iii).
Encodings:: BibTeX

…

9: 3.5 Quadrature

… ►The monic and orthonormal recursion relations of this section are both closely related to the Lanczos recursion relation in §3.2(vi). …

10: 12.14 The Function $W\left(a,x\right)$

… ►where

\alpha_{n}(a)

and

\beta_{n}(a)

satisfy the recursion relations …