computation by recursion

SearchAdvancedHelp

(0.002 seconds)

11—20 of 21 matching pages

11: 18.39 Applications in the Physical Sciences

… ►The discrete variable representations (DVR) analysis is simplest when based on the classical OP’s with their analytically known recursion coefficients (Table 3.5.17_5), or those non-classical OP’s which have analytically known recursion coefficients, making stable computation of the $x_i$ and $w_i$, from the J-matrix as in §3.5(vi), straightforward. …Table 18.39.1 lists typical non-classical weight functions, many related to the non-classical Freud weights of §18.32, and §32.15, all of which require numerical computation of the recursion coefficients (i. …

12: 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. …

13: Bibliography L

… ►

Co-recursive associated Jacobi polynomials. J. Comput. Appl. Math. 57 (1-2), pp. 203–213.

ⓘ

External Links:

ISSN 0377-0427, Document, MathReview, ZentralBlatt

Referenced by:

§18.30(i).

Encodings:

BibTeX

…

14: 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. …

15: 27.20 Methods of Computation: Other Number-Theoretic Functions

§27.20 Methods of Computation: Other Number-Theoretic Functions

… ►The recursion formulas (27.14.6) and (27.14.7) can be used to calculate the partition function $p\left(n\right)$ for . …To compute a particular value $p\left(n\right)$ it is better to use the Hardy–Ramanujan–Rademacher series (27.14.9). … ►A recursion formula obtained by differentiating (27.14.18) can be used to calculate Ramanujan’s function $\tau \left(n\right)$, and the values can be checked by the congruence (27.14.20). …

16: 9.19 Approximations

… ►

Corless et al. (1992) describe a method of approximation based on subdividing $ℂ$ into a triangular mesh, with values of $\mathrm{Ai}\left(z\right)$, ${\mathrm{Ai}}^{\prime }\left(z\right)$ stored at the nodes. $\mathrm{Ai}\left(z\right)$ and ${\mathrm{Ai}}^{\prime }\left(z\right)$ are then computed from Taylor-series expansions centered at one of the nearest nodes. The Taylor coefficients are generated by recursion, starting from the stored values of $\mathrm{Ai}\left(z\right)$, ${\mathrm{Ai}}^{\prime }\left(z\right)$ at the node. Similarly for $\mathrm{Bi}\left(z\right)$, ${\mathrm{Bi}}^{\prime }\left(z\right)$.

…

17: Bibliography S

… ►

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

ⓘ

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

External Links:

Document, Code 1, Code 2, Code 3

Referenced by:

8th item.

Encodings:

BibTeX

…

18: Bibliography M

… ►

Computation of inhomogeneous Airy functions. J. Comput. Appl. Math. 53 (1), pp. 109–116.

ⓘ

External Links:

ISSN 0377-0427, Document, MathReview (Dumitru Acu), ZentralBlatt

Referenced by:

1st item.

Encodings:

BibTeX

… ►

The efficient computation of some generalised exponential integrals. J. Comput. Appl. Math. 148 (2), pp. 363–374.

ⓘ

External Links:

ISSN 0377-0427, Document, MathReview, ZentralBlatt

Referenced by:

§8.19(v).

Encodings:

BibTeX

… ►

On the interval computation of elementary functions. C. R. Acad. Bulgare Sci. 34 (3), pp. 319–322.

ⓘ

External Links:

ISSN 0366-8681, MathReview (David F. Griffiths), ZentralBlatt

Referenced by:

§4.45(i).

Encodings:

BibTeX

… ►

The computation of elementary functions in radix $2^p$ . Computing 53 (3-4), pp. 219–232.

ⓘ

Notes:

International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics (Vienna, 1993)

External Links:

ISSN 0010-485X, Document, MathReview, ZentralBlatt

Referenced by:

§4.45(i).

Encodings:

BibTeX

… ►

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

…

19: 3.5 Quadrature

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

Example

… ► … ► …

20: Bibliography F

… ►

Theory and Computation of Spheroidal Harmonics with General Arguments. Master’s Thesis, The University of Western Australia, Department of Physics.

ⓘ

Notes:

Contains Mathematica package for spheroidal wave functions of complex arguments with complex parameters.

External Links:

FullText

Referenced by:

§30.12, 1st item, 2nd item.

Encodings:

BibTeX

►

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

ⓘ

Notes:

Fortran for exact calculation using integers

External Links:

ISSN 0010-4655, Document, Code, MathReview Entry

Referenced by:

§34.13, §34.13, 5th item.

Encodings:

BibTeX

… ►

Faster computation of Bernoulli numbers. J. Algorithms 13 (3), pp. 431–445.

ⓘ

External Links:

ISSN 0196-6774, MathReview (P. K. Subramanian), ZentralBlatt

Referenced by:

§24.19(i).

Encodings:

BibTeX

… ►

Computing the hypergeometric function. J. Comput. Phys. 137 (1), pp. 79–100.

ⓘ

Notes:

Double-precision Fortran

External Links:

ISSN 0021-9991, Document, Code, MathReview (J. P. Singhal), ZentralBlatt

Referenced by:

§15.19(i), 1st item, 2nd item.

Encodings:

BibTeX

… ►

On the coefficients in the recursion formulae of orthogonal polynomials. Proc. Roy. Irish Acad. Sect. A 76 (1), pp. 1–6.

ⓘ

External Links:

MathReview (A. G. Law), ZentralBlatt

Referenced by:

§18.32, §32.15.

Encodings:

BibTeX

…