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11: Viewing DLMF Interactive 3D Graphics

… ►Below we provide some notes and links to online material which might be helpful in viewing our visualizations, but please see our Disclaimer. …

12: Foreword

… ►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. …

13: 3.12 Mathematical Constants

… ►For access to online high-precision numerical values of mathematical constants see Sloane (2003). …

14: Bibliography L

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Some differential equations and associated integral equations. Quart. J. Math. (Oxford) 5, pp. 81–97.

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External Links:

Document, ZentralBlatt

Referenced by:

§31.10(i), §31.9(i).

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Moment-theory investigations of photoabsorption and dispersion profiles in atoms and ions. Phys. Rev. A 14, pp. 1042–1056.

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External Links:

Document, Link

Referenced by:

§18.40(ii).

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Numerical Evaluation of Special Functions. In Mathematics of Computation 1943–1993: A Half-Century of Computational Mathematics (Vancouver, BC, 1993), Proc. Sympos. Appl. Math., Vol. 48, pp. 79–125.

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Notes:

An updated version exists online.

External Links:

FullText, MathReview (John P. Coleman), ZentralBlatt

Referenced by:

Ch.3.

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Theory of the fourth Painlevé equation. Differ. Uravn. 3 (5), pp. 771–780 (Russian).

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Notes:

In Russian. English translation: Differential Equations 3(5), pp. 395–399

External Links:

MathReview (Z. Nehari), ZentralBlatt

Referenced by:

§32.10(iv), §32.7(iv), §32.8(iv).

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Jacobi polynomial expansions of a generalized hypergeometric function over a semi-infinite ray. Math. Comp. 17 (84), pp. 395–404.

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External Links:

FullText, MathReview (I. A. Stegun), ZentralBlatt

Referenced by:

2nd item.

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15: Bonita V. Saunders

Profile
Bonita V. Saunders

… ►As the principal developer of graphics for the DLMF, she has collaborated with other NIST mathematicians, computer scientists, and student interns to produce informative graphs and dynamic interactive visualizations of elementary and higher mathematical functions over both simply and multiply connected domains. …

16: Bibliography M

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Hypergeometric Functions.

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Notes:

Unpublished Lecture Notes, University of London. An online version exists.

External Links:

FullText

Referenced by:

§35.7(ii), §35.8(iii).

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Catastrophe optics of spheroidal drops and generalized rainbows. J. Quantit. Spec. and Rad. Trans. 63, pp. 341–351.

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External Links:

Document

Referenced by:

§36.14(ii).

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On the evaluation of the integral over the product of two spherical Bessel functions. J. Math. Phys. 32 (3), pp. 642–648.

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External Links:

ISSN 0022-2488, Document, MathReview (S. K. Chatterjea), ZentralBlatt

Referenced by:

§1.17(ii), §10.59.

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Mathieu Functions and Spheroidal Functions and Their Mathematical Foundations: Further Studies. Lecture Notes in Mathematics, Vol. 837, Springer-Verlag, Berlin-New York.

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External Links:

ISBN 3-540-10282-5, 0-387-10282-5, MathReview (R. A. Askey), ZentralBlatt

Referenced by:

§28.10(ii), §28.11, §28.2(v), §28.27, §28.28(i), §28.28(v), §28.30(ii), §28.6(i), §28.6(i), §28.6(i), §28.7, §28.7, Ch.28, §30.11(vi), §30.12, §30.13(v), §30.14(v), §30.15(i), §30.3(iv), Ch.30, Profile Gerhard Wolf.

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Aspects of Multivariate Statistical Theory. John Wiley & Sons Inc., New York.

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External Links:

ISBN 0-471-09442-0, MathReview (Nariaki Sugiura), ZentralBlatt

Referenced by:

§35.11, §35.2, §35.4(i), §35.4(ii), §35.6(i), §35.6(ii), §35.7(i), §35.7(ii), §35.7(iii), §35.7(iv), §35.8(i), §35.8(ii), §35.8(iv), §35.9, Ch.35, Profile Robb J. Muirhead.

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17: Notices

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Within each of the DLMF chapters themselves we will provide a list of research software for the functions discussed in that chapter. The purpose of these listings is to provide references to the research literature on the engineering of software for special functions. To qualify for listing, the development of the software must have been the subject of a research paper published in the peer-reviewed literature. If such software is available online for free download we will provide a link to the software.

In general, we will not index other software within DLMF chapters unless the software is unique in some way, such as being the only known software for computing a particular function.

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18: Philip J. Davis

Profile
Philip J. Davis

… ►In 1957, Davis took over as Chief, Numerical Analysis Section when John Todd and his wife Olga Taussky-Todd, feeling a strong pull toward teaching and research, left to pursue full-time positions at the California Institute of Technology. … ►NBS mathematician Irene Stegun took over management of the A&S project which was already well on its way, and led the work to publication in 1964. … ►Davis’s comments about our uninspired graphs sparked the research and design of techniques for creating interactive 3D visualizations of function surfaces, which grew in sophistication as our knowledge and the technology for developing 3D graphics on the web advanced over the years. …

19: Richard A. Askey

Profile
Richard A. Askey

… ►Over his career his primary research areas were in Special Functions and Orthogonal Polynomials, but also included other topics from Classical Analysis and related areas. … ►

5 Gamma Function

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20: Bibliography D

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Bernoulli Numbers. Bibliography (1713–1990). Queen’s Papers in Pure and Applied Mathematics, Vol. 87, Queen’s University, Kingston, ON.

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Notes:

A frequently updated version, with links to reviews, exists online

External Links:

Online version, MathReview, ZentralBlatt

Referenced by:

Ch.24.

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A simple sum formula for Clebsch-Gordan coefficients. Lett. Math. Phys. 5 (3), pp. 207–211.

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External Links:

ISSN 0377-9017, Document, MathReview, ZentralBlatt

Referenced by:

§14.17(iv).

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From Nonlinearity to Coherence: Universal Features of Nonlinear Behaviour in Many-Body Physics. Oxford University Press, Oxford.

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Referenced by:

Profile Peter A. Clarkson.

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Special Functions. World Scientific Publishing Co., Inc., River Edge, NJ.

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External Links:

ISBN 981-02-4393-6, Document, Link, MathReview Entry

Referenced by:

Profile Mourad E.H. Ismail.

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The incomplete beta function—a historical profile. Arch. Hist. Exact Sci. 24 (1), pp. 11–29.

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External Links:

ISSN 0003-9519, MathReview (Willard Parker), ZentralBlatt

Referenced by:

§8.17(i).

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