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1: 24.1 Special Notation
Bernoulli Numbers and Polynomials
The origin of the notation B n , B n ( x ) , is not clear. …
Euler Numbers and Polynomials
Its coefficients were first studied in Euler (1755); they were called Euler numbers by Raabe in 1851. The notations E n , E n ( x ) , as defined in §24.2(ii), were used in Lucas (1891) and Nörlund (1924). …
2: Customize DLMF
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3: Preface
The new DLMF (Digital Library of Mathematical Functions) will appear in a hardcover edition and as a free electronic publication on the World Wide Web. The authors will review the relevant published literature and produce approximately twice the number of formulas that were contained in the original Handbook. …
4: About MathML
, built-in to the browser) support for MathML is growing, (see Browsers supporting MathML). …By default, DLMF will use Native support when available; You may choose how MathML is processed (Native or MathJax) at Customize DLMF. In rare cases, a browser lacks both MathML support and a robust enough javascript implementation capable of running MathJax; you may wish to visit the Customize DLMF page and choose the HTML+images document format. …
Browsers supporting MathML
Recent enhancements to the WebKit engine now provide support for MathML Core. …
5: About the Project
The results have been published in book form as the NIST Handbook of Mathematical Functions, by Cambridge University Press, and disseminated in the free electronic Digital Library of Mathematical Functions. … Since that time there have been a number of developments. … For acknowledgements of financial support see Funding.
6: 31.14 General Fuchsian Equation
The general second-order Fuchsian equation with N + 1 regular singularities at z = a j , j = 1 , 2 , , N , and at , is given by
31.14.1 d 2 w d z 2 + ( j = 1 N γ j z a j ) d w d z + ( j = 1 N q j z a j ) w = 0 , j = 1 N q j = 0 .
The three sets of parameters comprise the singularity parameters a j , the exponent parameters α , β , γ j , and the N 2 free accessory parameters q j . With a 1 = 0 and a 2 = 1 the total number of free parameters is 3 N 3 . …
31.14.3 w ( z ) = ( j = 1 N ( z a j ) γ j / 2 ) W ( z ) ,
7: Bibliography N
  • W. Narkiewicz (2000) The Development of Prime Number Theory: From Euclid to Hardy and Littlewood. Springer-Verlag, Berlin.
  • M. Neher (2007) Complex standard functions and their implementation in the CoStLy library. ACM Trans. Math. Softw. 33 (1), pp. Article 2.
  • NetNUMPAC (free Fortran library)
  • NMS (free collection of Fortran subroutines)
  • Number Theory Web (website)
  • 8: 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.

  • NIST does not provide support of any kind for software indexed in the DLMF. …
    9: DLMF Project News
    error generating summary
    10: Browsers
    Most modern browsers support either MathML, or the MathJax fallback acceptably; If yours does not, please consider upgrading. …If none of those solutions work for you, you may explicitly choose a format such as HTML+images, using images for mathematics, at Customize DLMF. …