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1: Software Index
  • Open Source Collections and Systems.

    These are collections of software (e.g. libraries) or interactive systems of a somewhat broad scope. Contents may be adapted from research software or may be contributed by project participants who donate their services to the project. The software is made freely available to the public, typically in source code form. While formal support of the collection may not be provided by its developers, within active projects there is often a core group who donate time to consider bug reports and make updates to the collection.

  • 2: 4.41 Sums
    For sums of hyperbolic functions see Gradshteyn and Ryzhik (2000, Chapter 1), Hansen (1975, §43), Prudnikov et al. (1986a, §5.3), and Zucker (1979).
    3: 7.2 Definitions
    4: 6.6 Power Series
    5: 26.2 Basic Definitions
    Table 26.2.1: Partitions p ( n ) .
    n p ( n ) n p ( n ) n p ( n )
    9 30 26 2436 43 63261
    6: 12.7 Relations to Other Functions
    For these, the corresponding results for U ( a , z ) with a = 2 , ± 3 , 1 2 , 3 2 , 5 2 , and the corresponding results for V ( a , z ) with a = 0 , ± 1 , ± 2 , ± 3 , 1 2 , 3 2 , 5 2 , see Miller (1955, pp. 42–43 and 77–79). …
    7: 27.2 Functions
    Table 27.2.1: Primes.
    n p n p n + 10 p n + 20 p n + 30 p n + 40 p n + 50 p n + 60 p n + 70 p n + 80 p n + 90
    4 7 43 89 139 193 251 311 373 433 491
    Table 27.2.2: Functions related to division.
    n ϕ ( n ) d ( n ) σ ( n ) n ϕ ( n ) d ( n ) σ ( n ) n ϕ ( n ) d ( n ) σ ( n ) n ϕ ( n ) d ( n ) σ ( n )
    4 2 3 7 17 16 2 18 30 8 8 72 43 42 2 44
    8: Bibliography N
  • J. N. Newman (1984) Approximations for the Bessel and Struve functions. Math. Comp. 43 (168), pp. 551–556.
  • N. E. Nörlund (1922) Mémoire sur les polynomes de Bernoulli. Acta Math. 43, pp. 121–196 (French).
  • 9: 10.39 Relations to Other Functions
    For these and further results see Miller (1955, pp. 42–43 and 77–79). …
    10: 10.73 Physical Applications
    See Jackson (1999, Chapter 3, §§3.7, 3.8, 3.11, 3.13), Lamb (1932, Chapter V, §§100–102; Chapter VIII, §§186, 191–193; Chapter X, §§303, 304), Happel and Brenner (1973, Chapter 3, §3.3; Chapter 7, §7.3), Korenev (2002, Chapter 4, §43), and Gray et al. (1922, Chapter XI). …