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21: 31.7 Relations to Other Functions

… ►Other reductions of $H\mathrm{\ell }$ to a ${}_2{}^{}F_1^{}$, with at least one free parameter, exist iff the pair $(a,p)$ takes one of a finite number of values, where $q=\alpha \beta p$. …

22: 22.19 Physical Applications

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Figure 22.19.1: Jacobi’s amplitude function $\mathrm{am}(x,k)$ for $0\le x\le 10\pi$ and $k=0.5,0.9999,1.0001,2$. When , $\mathrm{am}(x,k)$ increases monotonically indicating that the motion of the pendulum is unbounded in $\theta$, corresponding to free rotation about the fulcrum; compare Figure 22.16.1. … Magnify

… ►The classical rotation of rigid bodies in free space or about a fixed point may be described in terms of elliptic, or hyperelliptic, functions if the motion is integrable (Audin (1999, Chapter 1)). …

23: Bibliography P

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Notes:

Computer algebra system designed for computations in number theory. Many transcendental functions are also included. PARI is also available as a C library to allow for faster computations. Originally developed by Henri Cohen and co-workers at the Université Bordeaux I.

External Links:

Home Page

Referenced by:

§ ‣ 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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24: Bibliography R

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Notes:

Symbolic and extended-precision general purpose computer algebra system.

External Links:

Home Page

Referenced by:

§ ‣ Software Cross Index.

Encodings:

BibTeX

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25: Bibliography W

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Surface Waves. In Handbuch der Physik, Vol. 9, Part 3, pp. 446–778.

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External Links:

Online edition, MathReview (F. Ursell), ZentralBlatt

Referenced by:

§11.12.

Encodings:

BibTeX

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Notes:

A free resource from Wolfram Research built with Mathematica technology.

External Links:

Home Page

Referenced by:

8th item, § ‣ Software Cross Index.

Encodings:

BibTeX

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26: Bibliography S

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Notes:

SAGE is a free open-source mathematics software system licensed under the GPL. It combines the power of many existing open-source packages into a common Python-based interface.

External Links:

Home Page

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, § ‣ 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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Notes:

The SLATEC Common Math Library is a large general purpose mathematical software library with broad coverage of elementary and special functions. Implementations in both single and double precision are provided. Developed by a consortium of US national laboratories. See Buzbee (1984).

External Links:

GAMS (package SLATEC)

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.

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27: Bibliography G

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Evaluation of $q$-gamma function and $q$-analogues by iterative algorithms. Numer. Algorithms 49 (1-4), pp. 159–168.

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External Links:

ISSN 1017-1398, Document, FullText, MathReview (Necdet Batir), ZentralBlatt

Referenced by:

§17.18, §17.18, §5.21, §5.21.

Encodings:

BibTeX

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GNU Scientific Library The GNU Project.

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Notes:

The GNU Scientific Library is a large general purpose numerical software library with broad coverage of elementary and special functions. Implementation is in double precision.

External Links:

Home Page

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.

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28: Foreword

… ►The document you are now holding, or the Web page you are now reading, represents an effort to extend the legacy of A&S well into the 21st century. …The online version, the NIST Digital Library of Mathematical Functions (DLMF), presents the same technical information along with extensions and innovative interactive features consistent with the new medium. …

29: Bibliography K

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Numerical Methods and Software. Prentice Hall, Englewood Cliffs, N.J..

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Notes:

Includes collection of single- and double-precision Fortran subroutines.

External Links:

ISBN 0-13-627258-4, GAMS (package NMS), ZentralBlatt

Referenced by:

NMS (free collection of Fortran subroutines).

Encodings:

BibTeX

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Algorithm 910: a portable C++ multiple-precision system for special-function calculations. ACM Trans. Math. Software 37 (4), pp. Art. 45, 27.

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Notes:

This system provides a uniform interface in C++, named e_float, to perform arithmetic operations and to calculate mathematical functions that are implemented in several different MP packages. It is a free, open-source, multiple precision package that allows the computation of many special functions. It supports calculations with 30….300 decimal digits and is interoperable with Microsoft’s CLR, Python and Mathematica.

External Links:

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

Referenced by:

Erratum (V1.0.9) for References, § ‣ 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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30: 3.8 Nonlinear Equations

… ►For other efficient derivative-free methods, see Le (1985). …