About the Project

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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
  • 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

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

    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: Bibliography B
  • 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.
  • 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
  • G. M. D’Ariano, C. Macchiavello, and M. G. A. Paris (1994) Detection of the density matrix through optical homodyne tomography without filtered back projection. Phys. Rev. A 50 (5), pp. 4298–4302.
  • K. Dilcher, L. Skula, and I. Sh. Slavutskiǐ (1991) Bernoulli Numbers. Bibliography (1713–1990). Queen’s Papers in Pure and Applied Mathematics, Vol. 87, Queen’s University, Kingston, ON.
  • O. Dragoun and G. Heuser (1971) A program to calculate internal conversion coefficients for all atomic shells without screening. Comput. Phys. Comm. 2 (7), pp. 427–432.