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1: 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
11 56 28 3718 45 89134
13 101 30 5604 47 1 24754
2: 26.9 Integer Partitions: Restricted Number and Part Size
Table 26.9.1: Partitions p k ( n ) .
n k
6 0 1 4 7 9 10 11 11 11 11 11
7 0 1 4 8 11 13 14 15 15 15 15
9 0 1 5 12 18 23 26 28 29 30 30
3: 11 Struve and Related Functions
Chapter 11 Struve and Related Functions
4: Staff
  • Richard B. Paris, University of Abertay, Chaps. 8, 11

  • Gerhard Wolf, University of Duisberg-Essen, Chap. 28

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

  • Simon Ruijsenaars, University of Leeds, for Chaps. 5, 28

  • 5: 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
    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 )
    2 1 2 3 15 8 4 24 28 12 6 56 41 40 2 42
    3 2 2 4 16 8 5 31 29 28 2 30 42 12 8 96
    11 10 2 12 24 8 8 60 37 36 2 38 50 20 6 93
    12 4 6 28 25 20 3 31 38 18 4 60 51 32 4 72
    6: 28 Mathieu Functions and Hill’s Equation
    Chapter 28 Mathieu Functions and Hill’s Equation
    7: Bibliography G
  • W. Gautschi (1966) Algorithm 292: Regular Coulomb wave functions. Comm. ACM 9 (11), pp. 793–795.
  • W. Gautschi (1969) Algorithm 363: Complex error function. Comm. ACM 12 (11), pp. 635.
  • A. Gervois and H. Navelet (1984) Some integrals involving three Bessel functions when their arguments satisfy the triangle inequalities. J. Math. Phys. 25 (11), pp. 3350–3356.
  • H. W. Gould (1960) Stirling number representation problems. Proc. Amer. Math. Soc. 11 (3), pp. 447–451.
  • V. I. Gromak (1975) Theory of Painlevé’s equations. Differ. Uravn. 11 (11), pp. 373–376 (Russian).
  • 8: 24.2 Definitions and Generating Functions
    Table 24.2.3: Bernoulli numbers B n = N / D .
    n N D B n
    28 2 37494 61029 870 2.72982 3107 ×10⁷
    Table 24.2.4: Euler numbers E n .
    n E n
    28 12522 59641 40362 98654 68285
    Table 24.2.5: Coefficients b n , k of the Bernoulli polynomials B n ( x ) = k = 0 n b n , k x k .
    k
    n 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
    11 0 5 6 0 11 2 0 11 0 11 0 55 6 11 2 1
    Table 24.2.6: Coefficients e n , k of the Euler polynomials E n ( x ) = k = 0 n e n , k x k .
    k
    n 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
    9: Bibliography P
  • R. B. Paris and A. D. Wood (1995) Stokes phenomenon demystified. Bull. Inst. Math. Appl. 31 (1-2), pp. 21–28.
  • J. B. Parkinson (1969) Optical properties of layer antiferromagnets with K 2 NiF 4 structure. J. Phys. C: Solid State Physics 2 (11), pp. 2012–2021.
  • R. Piessens and M. Branders (1984) Algorithm 28. Algorithm for the computation of Bessel function integrals. J. Comput. Appl. Math. 11 (1), pp. 119–137.
  • G. P. M. Poppe and C. M. J. Wijers (1990) Algorithm 680: Evaluation of the complex error function. ACM Trans. Math. Software 16 (1), pp. 47.
  • 10: 26.3 Lattice Paths: Binomial Coefficients
    Table 26.3.1: Binomial coefficients ( m n ) .
    m n
    8 1 8 28 56 70 56 28 8 1
    Table 26.3.2: Binomial coefficients ( m + n m ) for lattice paths.
    m n
    2 1 3 6 10 15 21 28 36 45
    6 1 7 28 84 210 462 924 1716 3003