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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: Viewing DLMF Interactive 3D Graphics
WebGL is supported in the current versions of most common web browsers. … 1, some advanced features of X3DOM are currently not fully supported (see x3dom.org). Until these issues are resolved we cannot guarantee that the DLMF WebGL visualizations can be viewed in Internet Explorer. … After installing the viewer you must select Customize DLMF on the DLMF Menu bar and choose either VRML or X3D under “Visualization Format. … Please see caniuse.com/webgl or x3dom.org for information on WebGL browser support.
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  • 4: Bibliography X
  • H. Xiao, V. Rokhlin, and N. Yarvin (2001) Prolate spheroidal wavefunctions, quadrature and interpolation. Inverse Problems 17 (4), pp. 805–838.
  • 5: DLMF Project News
    error generating summary
    6: 27.18 Methods of Computation: Primes
    §27.18 Methods of Computation: Primes
    An overview of methods for precise counting of the number of primes not exceeding an arbitrary integer x is given in Crandall and Pomerance (2005, §3.7). …An analytic approach using a contour integral of the Riemann zeta function (§25.2(i)) is discussed in Borwein et al. (2000). … These algorithms are used for testing primality of Mersenne numbers, 2 n 1 , and Fermat numbers, 2 2 n + 1 . …
    7: 26.11 Integer Partitions: Compositions
    c ( n ) denotes the number of compositions of n , and c m ( n ) is the number of compositions into exactly m parts. c ( T , n ) is the number of compositions of n with no 1’s, where again T = { 2 , 3 , 4 , } . …
    26.11.1 c ( 0 ) = c ( T , 0 ) = 1 .
    The Fibonacci numbers are determined recursively by … Additional information on Fibonacci numbers can be found in Rosen et al. (2000, pp. 140–145).
    8: Mathematical Introduction
    The NIST Handbook has essentially the same objective as the Handbook of Mathematical Functions that was issued in 1964 by the National Bureau of Standards as Number 55 in the NBS Applied Mathematics Series (AMS). …
    ( a , b ] or [ a , b ) half-closed intervals.
    set of all positive integers.
    set of all rational numbers.
    For equations or other technical information that appeared previously in AMS 55, the DLMF usually includes the corresponding AMS 55 equation number, or other form of reference, together with corrections, if needed. …
    9: 26.6 Other Lattice Path Numbers
    §26.6 Other Lattice Path Numbers
    Delannoy Number D ( m , n )
    Motzkin Number M ( n )
    Narayana Number N ( n , k )
    §26.6(iv) Identities
    10: 24.15 Related Sequences of Numbers
    §24.15 Related Sequences of Numbers
    §24.15(i) Genocchi Numbers
    §24.15(ii) Tangent Numbers
    §24.15(iii) Stirling Numbers
    §24.15(iv) Fibonacci and Lucas Numbers