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1: 27.18 Methods of Computation: Primes

… ► Oliveira e Silva has calculated $\pi \left(x\right)$ for $x={10}^{23}$, using the combinatorial methods of Lagarias et al. (1985) and Deléglise and Rivat (1996); see Oliveira e Silva (2006). …

2: Bibliography O

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Tables of Laplace Transforms. Springer-Verlag, Berlin-New York.

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Notes:

Table errata: Math. Comp. v. 50 (1988), no. 182, pp. 653–654.

External Links:

ISBN 0-387-06350-1, MathReview, ZentralBlatt

Referenced by:

§1.14(viii), §10.22(vi), §10.43(vi), §11.5(iii), §11.7(v), §11.9(iv), §12.12, §12.5(iv), §13.10(ii), §13.23(i), §14.17(v), §15.14, §18.17(ix), §20.10(ii), §5.13, §6.14(iii), §6.7(iv), §7.14(iii), §7.7(iii), §8.6(iii).

Encodings:

BibTeX

… ►

Computing $\pi (x)$: The combinatorial method. Revista do DETUA 4 (6), pp. 759–768.

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Notes:

Online fulltext contains postpublication annotations.

External Links:

FullText

Referenced by:

§27.18.

Encodings:

BibTeX

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3: Foreword

… ►That 1046-page tome proved to be an invaluable reference for the many scientists and engineers who use the special functions of applied mathematics in their day-to-day work, so much so that it became the most widely distributed and most highly cited NIST publication in the first 100 years of the institution’s existence. … ►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. …

4: Notices

… ►As a condition of using the DLMF, you explicitly release NIST from any and all liabilities for any damage of any type that may result from errors or omissions in the DLMF. … ►

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.

…

5: Possible Errors in DLMF

… ►Errors in the printed Handbook may already have been corrected in the online version; please consult Errata. …

6: How to Cite

… ►The direct correspondence between the reference numbers in the printed Handbook and the permalinks used online in the DLMF enables readers of either version to cite specific items and their readers to easily look them up again — in either version! ►The following table outlines the correspondence between reference numbers as they appear in the Handbook, and the URL’s that find the same item online. …

7: Frank W. J. Olver

… ►A highly regarded expositor, Olver was author of more than 100 technical articles. … ►Most notably, he served as the Editor-in-Chief and Mathematics Editor of the online NIST Digital Library of Mathematical Functions and its 966-page print companion, the NIST Handbook of Mathematical Functions (Cambridge University Press, 2010). …

8: Bibliography U

… ►

Mathematics of Computation Unpublished Mathematical Tables Collection.

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Notes:

Archives of American Mathematics, Center for American History, The University of Texas at Austin. Covers 1944–1994. An online guide is arranged chronologically by date of issuance within Mathematics of Computation

External Links:

Guide

Referenced by:

§27.21.

Encodings:

BibTeX

… ►

Collisions and umbilic catastrophes. The hyperbolic umbilic canonical diffraction integral. Molecular Phys. 50 (6), pp. 1215–1230.

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External Links:

ISSN 0026-8976, Document, MathReview (D. R. J. Chillingworth)

Referenced by:

§36.14(iii).

Encodings:

BibTeX

9: 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. …

10: 3.12 Mathematical Constants

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