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1: Possible Errors in DLMF
Errors in the printed Handbook may already have been corrected in the online version; please consult Errata. …
2: 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. …
3: 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. …
4: 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. …
5: 3.12 Mathematical Constants
For access to online high-precision numerical values of mathematical constants see Sloane (2003). …
6: Notices
  • Index of Selected Software Within the DLMF Chapters

    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.

  • 7: Bibliography U
  • Unpublished Mathematical Tables (1944) Mathematics of Computation Unpublished Mathematical Tables Collection.
  • 8: Frank W. J. Olver
    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). …
    9: About the Project
    They were selected as recognized leaders in the research communities interested in the mathematics and applications of special functions and orthogonal polynomials; in the presentation of mathematics reference information online and in handbooks; and in the presentation of mathematics on the web. …
    10: Errata
  • Subsection 25.10(ii)

    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).

  • Equation (3.3.34)

    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

  • Table 22.4.3

    Originally a minus sign was missing in the entries for cd u and dc u in the second column (headed z + K + i K ). The correct entries are k 1 ns z and k 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 sn , cn , dn , whereas Table 22.4.3 covers all 12 Jacobian elliptic functions.

    u
    z + K z + K + i K z + i K z + 2 K z + 2 K + 2 i K z + 2 i K
    cd u sn z k 1 ns z k 1 dc z cd z cd z cd z
    dc u ns z k sn z k cd z dc z dc z dc z

    Reported 2014-02-28 by Svante Janson.

  • References

    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.