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1: 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).
2: 7.2 Definitions
3: 6.6 Power Series
4: 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
5: 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). …
6: 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
7: 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).
  • 8: 10.39 Relations to Other Functions
    For these and further results see Miller (1955, pp. 42–43 and 77–79). …
    9: 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). …
    10: 19.1 Special Notation
    We use also the function D ( ϕ , k ) , introduced by Jahnke et al. (1966, p. 43). …