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1: 10 Bessel Functions
Chapter 10 Bessel Functions
2: 11 Struve and Related Functions
Chapter 11 Struve and Related Functions
3: 29 Lamé Functions
Chapter 29 Lamé Functions
4: Staff
  • Leonard C. Maximon, George Washington University, Chaps. 10, 34

  • Richard B. Paris, University of Abertay, Chaps. 8, 11

  • Hans Volkmer, University of Wisconsin, Milwaukee, Chaps. 29, 30

  • Richard B. Paris, University of Abertay Dundee, for Chaps. 8, 11

  • Hans Volkmer, University of Wisconsin–Milwaukee, for Chaps. 29, 30

  • 5: Publications
  • B. V. Saunders and Q. Wang (2005) Boundary/Contour Fitted Grid Generation for Effective Visualizations in a Digital Library of Mathematical Functions, Proceedings of the 9th International Conference on Numerical Grid Generation in Computational Field Simulations, San Jose, June 11–18, 2005. pp. 61–71. PDF
  • Q. Wang and B. V. Saunders (2005) Web-Based 3D Visualization in a Digital Library of Mathematical Functions, Proceedings of the Web3D Symposium, Bangor, UK, March 29–April 1, 2005. PDF
  • B. V. Saunders and Q. Wang (2006) From B-Spline Mesh Generation to Effective Visualizations for the NIST Digital Library of Mathematical Functions, in Curve and Surface Design, Proceedings of the Sixth International Conference on Curves and Surfaces, Avignon, France June 29–July 5, 2006, pp. 235–243. PDF
  • 6: 26.2 Basic Definitions
    Table 26.2.1: Partitions p ( n ) .
    n p ( n ) n p ( n ) n p ( n )
    6 11 23 1255 40 37338
    10 42 27 3010 44 75175
    11 56 28 3718 45 89134
    12 77 29 4565 46 1 05558
    7: 26.9 Integer Partitions: Restricted Number and Part Size
    Table 26.9.1: Partitions p k ( n ) .
    n k
    0 1 2 3 4 5 6 7 8 9 10
    6 0 1 4 7 9 10 11 11 11 11 11
    7 0 1 4 8 11 13 14 15 15 15 15
    8 0 1 5 10 15 18 20 21 22 22 22
    9 0 1 5 12 18 23 26 28 29 30 30
    8: 1 Algebraic and Analytic Methods
    9: 25.20 Approximations
  • Cody et al. (1971) gives rational approximations for ζ ( s ) in the form of quotients of polynomials or quotients of Chebyshev series. The ranges covered are 0.5 s 5 , 5 s 11 , 11 s 25 , 25 s 55 . Precision is varied, with a maximum of 20S.

  • Antia (1993) gives minimax rational approximations for Γ ( s + 1 ) F s ( x ) , where F s ( x ) is the Fermi–Dirac integral (25.12.14), for the intervals < x 2 and 2 x < , with s = 1 2 , 1 2 , 3 2 , 5 2 . For each s there are three sets of approximations, with relative maximum errors 10 4 , 10 8 , 10 12 .

  • 10: 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
    5 11 47 97 149 197 257 313 379 439 499
    10 29 71 113 173 229 281 349 409 463 541
    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 )
    3 2 2 4 16 8 5 31 29 28 2 30 42 12 8 96
    9 6 3 13 22 10 4 36 35 24 4 48 48 16 10 124
    11 10 2 12 24 8 8 60 37 36 2 38 50 20 6 93