computation of coefficients

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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

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3: Bibliography S

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Recursive evaluation of $3j$- and $6j$- coefficients. Comput. Phys. Comm. 11 (2), pp. 269–278.

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Notes:

Double-precision Fortran provided in 3 parts, $j_1$-recursion for $3j$-coefficients, $m_2$-recursion for $3j$-coefficients, and $j_1$-recursion for $6j$-coefficients

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8th item.

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A new Fortran program for the $9$-$j$ angular momentum coefficient. Comput. Phys. Comm. 56 (2), pp. 231–248.

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Document, ZentralBlatt

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§34.13.

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New Fortran programs for angular momentum coefficients. Comput. Phys. Comm. 15 (3-4), pp. 227–235.

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§34.13.

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Computation of angular momentum coefficients using sets of generalized hypergeometric functions. Comput. Phys. Comm. 22 (2-3), pp. 297–302.

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§34.13.

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Root-rational-fraction package for exact calculation of vector-coupling coefficients. Comput. Phys. Comm. 21 (2), pp. 195–205.

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Notes:

Double-precision Fortran, maximum accuracy 16D

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10th item.

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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

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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 the scheme can be used in backward direction.

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6: Bibliography T

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Angular momentum coupling coefficients. Comput. Phys. Comm. 1 (5), pp. 337–342.

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Single-precision Fortran

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11st item.

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7: Bibliography F

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A computer program for the calculation of angular-momentum coupling coefficients. Comput. Phys. Comm. 70 (1), pp. 147–153.

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Notes:

Fortran for exact calculation using integers

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ISSN 0010-4655, Document, Code, MathReview Entry

Referenced by:

§34.13, §34.13, 5th item.

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8: 30.16 Methods of Computation

… ►The coefficients $a_{n,r}^m({\gamma }^2)$ are computed as the recessive solution of (30.8.4) (§3.6), and normalized via (30.8.5). … ►The coefficients $a_{n,k}^m({\gamma }^2)$ calculated in §30.16(ii) can be used to compute $S_n^{m(j)}(z,\gamma )$, $j=1,2,3,4$ from (30.11.3) as well as the connection coefficients $K_n^m(\gamma )$ from (30.11.10) and (30.11.11). …

9: Bibliography K

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Pascal program for generating tables of $\mathrm{SU}(3)$ Clebsch-Gordan coefficients. Comput. Phys. Comm. 85 (1), pp. 82–88.

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ISSN 0010-4655, Document, Code, MathReview Entry, ZentralBlatt

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6th item.

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10: Bibliography E

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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.

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ISSN 0098-3500, Document, FullText, MathReview Entry, ZentralBlatt

Referenced by:

3rd item, §28.36(iii).

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