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1: 25.10 Zeros

… ►More than 41% of all the zeros in the critical strip lie on the critical line (Bui et al. (2011)). …

2: 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. … ►WebGL is a JavaScript API (application programming interface) for rendering 3D graphics in a web browser without the use of a plugin. …

3: 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. … ►This could not have been done without the cooperation of many mathematicians, information technologists, and physical scientists both within NIST and externally. …

4: Errata

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In the paragraph immediately below (25.10.4), it was originally stated that “more than one-third of all zeros in the critical strip lie on the critical line.” which referred to Levinson (1974). This sentence has been updated with “one-third” being replaced with “41%” now referring to Bui et al. (2011) (suggested by Gergő Nemes on 2021-08-23).

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In the online version, the leading divided difference operators were previously omitted from these formulas, due to programming error.

Reported by Nico Temme on 2021-06-01

… ►These enable insertions of new numbered objects between existing ones without affecting their permanent identifiers and URLs. … ►

Originally a minus sign was missing in the entries for $\mathrm{cd}u$ and $\mathrm{dc}u$ in the second column (headed $z+K+i{K}^{\prime }$). The correct entries are $-k^{-1}\mathrm{ns}z$ and $-k\mathrm{sn}z$. Note: These entries appear online but not in the published print edition. More specifically, Table 22.4.3 in the published print edition is restricted to the three Jacobian elliptic functions $\mathrm{sn},\mathrm{cn},\mathrm{dn}$, whereas Table 22.4.3 covers all 12 Jacobian elliptic functions.

	$u$
	$z+K$	$z+K+\mathrm{i}{K}^{\prime }$	$z+\mathrm{i}{K}^{\prime }$	$z+2K$	$z+2K+2\mathrm{i}{K}^{\prime }$	$z+2\mathrm{i}{K}^{\prime }$
$\mathrm{⋮}$
$\mathrm{cd}u$	$-\mathrm{sn}z$	$-k^{-1}\mathrm{ns}z$	$k^{-1}\mathrm{dc}z$	$-\mathrm{cd}z$	$-\mathrm{cd}z$	$\mathrm{cd}z$
$\mathrm{⋮}$
$\mathrm{dc}u$	$-\mathrm{ns}z$	$-k\mathrm{sn}z$	$k\mathrm{cd}z$	$-\mathrm{dc}z$	$-\mathrm{dc}z$	$\mathrm{dc}z$
$\mathrm{⋮}$

Reported 2014-02-28 by Svante Janson.

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Bibliographic citations were added in §§3.5(iv), 4.44, 8.22(ii), 22.4(i), and minor clarifications were made in §§19.12, 20.7(vii), 22.9(i). In addition, several minor improvements were made affecting only ancilliary documents and links in the online version.

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5: Bibliography B

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More than 41% of the zeros of the zeta function are on the critical line. Acta Arith. 150 (1), pp. 35–64.

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External Links:

ISSN 0065-1036, Document, Link, MathReview (Timothy S. Trudgian), ZentralBlatt

Referenced by:

§25.10(ii), §25.10(ii), Erratum (V1.1.4) for Subsection 25.10(ii).

Encodings:

BibTeX

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6: Possible Errors in DLMF

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

7: 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. …

8: 3.12 Mathematical Constants

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

9: DLMF Project News

error generating summary

10: Bibliography D

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Detection of the density matrix through optical homodyne tomography without filtered back projection. Phys. Rev. A 50 (5), pp. 4298–4302.

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External Links:

Document

Referenced by:

§13.28(iii).

Encodings:

BibTeX

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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.

Encodings:

BibTeX

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A program to calculate internal conversion coefficients for all atomic shells without screening. Comput. Phys. Comm. 2 (7), pp. 427–432.

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Notes:

Single-precision Fortran

External Links:

Document, Code

Referenced by:

1st item.

Encodings:

BibTeX

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