computation to high precision via elliptic integrals

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1: 19.35 Other Applications

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§19.35(i) Mathematical

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2: Bibliography S

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Coulomb functions analytic in the energy. Comput. Phys. Comm. 25 (1), pp. 87–95.

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Notes:

Double-precision Fortran code.

External Links:

Document, Code

Referenced by:

§33.1, §33.14(iv), 9th item.

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BibTeX

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Numerical evaluation of spherical Bessel transforms via fast Fourier transforms. J. Comput. Phys. 100 (2), pp. 294–296.

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External Links:

ISSN 0021-9991, Document, MathReview, ZentralBlatt

Referenced by:

§10.74(vii).

Encodings:

BibTeX

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Algorithm 721: MTIEU1 and MTIEU2: Two subroutines to compute eigenvalues and solutions to Mathieu’s differential equation for noninteger and integer order. ACM Trans. Math. Software 19 (3), pp. 391–406.

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Notes:

Double-precision Fortran, maximum accuracy 18D

External Links:

ISSN 0098-3500, Document, GAMS (module 721; package TOMS), ZentralBlatt

Referenced by:

3rd item, 5th item.

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BibTeX

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On numerical Bessel transformation. Comput. Phys. Comm. 16 (3), pp. 383–387.

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Notes:

Single-precision Fortran, maximum accuracy 15D.

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ISSN 0010-4655, Document, Code

Referenced by:

8th item.

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BibTeX

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Automatic computing methods for special functions. II. The exponential integral $E_n(x)$ . J. Res. Nat. Bur. Standards Sect. B 78B, pp. 199–216.

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Notes:

Double-precision Fortran, maximum accuracy 16S.

External Links:

MathReview (Bernard H. Rosman), ZentralBlatt

Referenced by:

§8.25(v), §8.28(vi).

Encodings:

BibTeX

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3: Bibliography B

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A program for computing the Fermi-Dirac functions. Comput. Phys. Comm. 21 (3), pp. 315–322.

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Notes:

Double-precision Fortran, maximum accuracy 10D.

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Document, Code

Referenced by:

2nd item.

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BibTeX

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A program for computing the Riemann zeta function for complex argument. Comput. Phys. Comm. 20 (3), pp. 441–445.

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Notes:

Double-precision Fortran, maximum accuracy 10S.

External Links:

Document, Code, ZentralBlatt

Referenced by:

1st item.

Encodings:

BibTeX

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KLEIN: Coulomb functions for real $\lambda$ and positive energy to high accuracy. Comput. Phys. Comm. 24 (2), pp. 141–159.

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Notes:

Double-precision Fortran code for positive energies.

External Links:

Document, Code

Referenced by:

5th item, §33.23(vii), 1st item.

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BibTeX

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Fast multiple-precision evaluation of elementary functions. J. Assoc. Comput. Mach. 23 (2), pp. 242–251.

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External Links:

Document, MathReview (Amnon Barak), ZentralBlatt

Referenced by:

§4.45(i).

Encodings:

BibTeX

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A program to calculate a general recoupling coefficient. Comput. Phys. Comm. 1 (4), pp. 241–250.

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Notes:

Single-precision Fortran

External Links:

Document, Code

Referenced by:

3rd item.

Encodings:

BibTeX

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4: Bibliography

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Algorithm 804: Subroutines for the computation of Mathieu functions of integer orders. ACM Trans. Math. Software 26 (3), pp. 408–414.

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Notes:

Double-precision C++, minimum accuracy 14D

External Links:

ISSN 0098-3500, Document, GAMS (module 804; package TOMS)

Referenced by:

1st item, 1st item.

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BibTeX

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Monotonicity theorems and inequalities for the complete elliptic integrals. J. Comput. Appl. Math. 172 (2), pp. 289–312.

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External Links:

ISSN 0377-0427, Document, MathReview (Živorad Tomovski), ZentralBlatt

Referenced by:

§19.9(i).

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BibTeX

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Computation of exponential integrals. ACM Trans. Math. Software 6 (3), pp. 365–377.

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External Links:

ISSN 0098-3500, Document, MathReview (M. M. Chawla), ZentralBlatt

Referenced by:

§8.25(v).

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BibTeX

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Rational function approximations for Fermi-Dirac integrals. The Astrophysical Journal Supplement Series 84, pp. 101–108.

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Notes:

Double-precision Fortran, maximum precision 8D.

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ISSN 0067-0049, Document, Code

Referenced by:

5th item, 1st item.

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BibTeX

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Arb: A C Library for Arbitrary Precision Ball Arithmetic.

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Notes:

An extended-precision C code for special functions. The library uses arbitrary-precision ball arithmetic. Ball arithmetic is an efficient technique for performing numerical computations with automatic and rigorous tracking of error bounds. Arb is designed with computer algebra and computational number theory in mind, extending the principles behind FLINT to the domain of real and complex numbers.

Referenced by:

§ ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index.

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BibTeX

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5: Software Index

… ►In the list below we identify four main sources of software for computing special functions. … ►

This is software of narrow scope developed as a byproduct of a research project and subsequently made available at no cost to the public. The software is often meant to demonstrate new numerical methods or software engineering strategies which were the subject of a research project. When developed, the software typically contains capabilities unavailable elsewhere. While the software may be quite capable, it is typically not professionally packaged and its use may require some expertise. The software is typically provided as source code or via a web-based service, and no support is provided.

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Such software ranges from a collection of reusable software parts (e.g., a library) to fully functional interactive computing environments with an associated computing language. Such software is usually professionally developed, tested, and maintained to high standards. It is available for purchase, often with accompanying updates and consulting support.

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Software associated with papers published in the journal Computer Physics Communications.

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A cross index of mathematical software in use at NIST.