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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: Bibliography B
  • R. L. Bishop (1981) Rainbow over Woolsthorpe Manor. Notes and Records Roy. Soc. London 36 (1), pp. 3–11 (1 plate).
  • H. M. Bui, B. Conrey, and M. P. Young (2011) More than 41% of the zeros of the zeta function are on the critical line. Acta Arith. 150 (1), pp. 35–64.
  • 3: Possible Errors in DLMF
    One source of confusion, rather than actual errors, are some new functions which differ from those in Abramowitz and Stegun (1964) by scaling, shifts or constraints on the domain; see the Info box (click or hover over the [Uncaptioned image] icon) for links to defining formula. …Errors in the printed Handbook may already have been corrected in the online version; please consult Errata. …
    4: Errata
  • Chapters 1 Algebraic and Analytic Methods, 10 Bessel Functions, 14 Legendre and Related Functions, 18 Orthogonal Polynomials, 29 Lamé Functions

    Over the preceding two months, the subscript parameters of the Ferrers and Legendre functions, 𝖯 n , 𝖰 n , P n , Q n , 𝑸 n and the Laguerre polynomial, L n , were incorrectly displayed as superscripts. Reported by Roy Hughes on 2022-05-23

  • 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.

  • 5: 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. …
    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: 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. …
    9: 3.12 Mathematical Constants
    For access to online high-precision numerical values of mathematical constants see Sloane (2003). …
    10: DLMF Project News
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