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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: Bibliography O
  • K. Okamoto (1987b) Studies on the Painlevé equations. II. Fifth Painlevé equation P V . Japan. J. Math. (N.S.) 13 (1), pp. 47–76.
  • F. W. J. Olver (1977b) Connection formulas for second-order differential equations having an arbitrary number of turning points of arbitrary multiplicities. SIAM J. Math. Anal. 8 (4), pp. 673–700.
  • M. Onoe (1955) Formulae and Tables, The Modified Quotients of Cylinder Functions. Technical report Technical Report UDC 517.564.3:518.25, Vol. 4, Report of the Institute of Industrial Science, University of Tokyo, Institute of Industrial Science, Chiba City, Japan.
  • 3: Bibliography Y
  • T. Yoshida (1995) Computation of Kummer functions U ( a , b , x ) for large argument x by using the τ -method. Trans. Inform. Process. Soc. Japan 36 (10), pp. 2335–2342 (Japanese).
  • 4: Bibliography N
  • A. Nakamura (1996) Toda equation and its solutions in special functions. J. Phys. Soc. Japan 65 (6), pp. 1589–1597.
  • W. Narkiewicz (2000) The Development of Prime Number Theory: From Euclid to Hardy and Littlewood. Springer-Verlag, Berlin.
  • I. Niven, H. S. Zuckerman, and H. L. Montgomery (1991) An Introduction to the Theory of Numbers. 5th edition, John Wiley & Sons Inc., New York.
  • Number Theory Web (website)
  • 5: Guide to Searching the DLMF
  • term:

    a textual word, a number, or a math symbol.

  • phrase:

    any double-quoted sequence of textual words and numbers.

  • proximity operator:

    adj, prec/n, and near/n, where n is any positive natural number.

  • $ stands for any number of alphanumeric characters
    (the more conventional * is reserved for the multiplication operator)
    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: 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
    9: 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
    10: 26.5 Lattice Paths: Catalan Numbers
    §26.5 Lattice Paths: Catalan Numbers
    §26.5(i) Definitions
    C ( n ) is the Catalan number. …
    §26.5(ii) Generating Function
    §26.5(iii) Recurrence Relations