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1: Bibliography N

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Complex standard functions and their implementation in the CoStLy library. ACM Trans. Math. Softw. 33 (1), pp. Article 2.

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Notes:

For the software see CoStLy (free C-XSC library)

External Links:

ISSN 0098-3500, Document

Referenced by:

3rd item, CoStLy (free C-XSC library).

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Double precision. In Japanese, with some English.

External Links:

Home Page

Referenced by:

§ ‣ Software Cross Index.

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BibTeX

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Notes:

Single and double precision. See Kahaner et al. (1989).

External Links:

GAMS (package NMS)

Referenced by:

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

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High-frequency scattering by an impenetrable sphere. Ann. Physics 34 (1), pp. 23–95.

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External Links:

Document, MathReview (E. Ar)

Referenced by:

§14.31(iii).

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2: 9.15 Mathematical Applications

… ►Airy functions play an indispensable role in the construction of uniform asymptotic expansions for contour integrals with coalescing saddle points, and for solutions of linear second-order ordinary differential equations with a simple turning point. …

3: Howard S. Cohl

… ►In this regard, he has been exploring mathematical knowledge management and the digital expression of mostly unambiguous context-free full semantic information for mathematical formulae.

4: Preface

… ►The new DLMF (Digital Library of Mathematical Functions) will appear in a hardcover edition and as a free electronic publication on the World Wide Web. …

5: 17.17 Physical Applications

… ►In exactly solved models in statistical mechanics (Baxter (1981, 1982)) the methods and identities of §17.12 play a substantial role. … ►They were given this name because they play a role in quantum physics analogous to the role of Lie groups and special functions in classical mechanics. …

6: 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

… ►plays a prototypal role in classical mechanics (Lawden (1989, §5.2)), quantum mechanics (Schulman (1981, Chapter 29)), and quantum field theory (Pokorski (1987, p. 203), Parisi (1988, §14.6)). … ►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)). …

7: 19.13 Integrals of Elliptic Integrals

… ►Cvijović and Klinowski (1994) contains fractional integrals (with free parameters) for $F(\varphi ,k)$ and $E(\varphi ,k)$, together with special cases. …

8: 31.2 Differential Equations

… ►The parameters play different roles: $a$ is the singularity parameter; $\alpha ,\beta ,\gamma ,\delta ,ϵ$ are exponent parameters; $q$ is the accessory parameter. The total number of free parameters is six. …

9: Bibliography R

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A code to calculate (high order) Bessel functions based on the continued fractions method. Comput. Phys. Comm. 76 (3), pp. 381–388.

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Notes:

Double-precision Fortran, maximum accuracy 18D.

External Links:

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

Referenced by:

6th item.

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High precision Chebyshev expansions for Airy functions and their derivatives. Technical report University of Birmingham Computer Centre.

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3rd item.

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Symbolic and extended-precision general purpose computer algebra system.

External Links:

Home Page

Referenced by:

§ ‣ Software Cross Index.

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BibTeX

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10: 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.

Encodings:

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Smoothing of the Stokes phenomenon for high-order differential equations. Proc. Roy. Soc. London Ser. A 436, pp. 165–186.

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External Links:

ISSN 0962-8444, FullText, MathReview (F. W. J. Olver), ZentralBlatt

Referenced by:

§2.11(v).

Encodings:

BibTeX

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