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1: 26.7 Set Partitions: Bell Numbers
§26.7 Set Partitions: Bell Numbers
26.7.1 B ( 0 ) = 1 ,
Table 26.7.1: Bell numbers.
n B ( n ) n B ( n )
2: 26.1 Special Notation
( m n ) binomial coefficient.
B ( n ) Bell number.
3: Errata
  • Equation (26.7.6)
    26.7.6 B ( n + 1 ) = k = 0 n ( n k ) B ( k )

    Originally this equation appeared with B ( n ) in the summation, instead of B ( k ) .

    Reported 2010-11-07 by Layne Watson.

  • 4: Bibliography S
  • M. R. Schroeder (2006) Number Theory in Science and Communication: With Applications in Cryptography, Physics, Digital Information, Computing, and Self-Similarity. 4th edition, Springer-Verlag, Berlin.
  • I. Sh. Slavutskiĭ (1995) Staudt and arithmetical properties of Bernoulli numbers. Historia Sci. (2) 5 (1), pp. 69–74.
  • I. Sh. Slavutskiĭ (1999) About von Staudt congruences for Bernoulli numbers. Comment. Math. Univ. St. Paul. 48 (2), pp. 137–144.
  • D. Slepian and H. O. Pollak (1961) Prolate spheroidal wave functions, Fourier analysis and uncertainty. I. Bell System Tech. J. 40, pp. 43–63.
  • D. Slepian (1964) Prolate spheroidal wave functions, Fourier analysis and uncertainity. IV. Extensions to many dimensions; generalized prolate spheroidal functions. Bell System Tech. J. 43, pp. 3009–3057.
  • 5: Bibliography B
  • K. L. Bell and N. S. Scott (1980) Coulomb functions (negative energies). Comput. Phys. Comm. 20 (3), pp. 447–458.
  • B. C. Berndt (1975b) Periodic Bernoulli numbers, summation formulas and applications. In Theory and Application of Special Functions (Proc. Advanced Sem., Math. Res. Center, Univ. Wisconsin, Madison, Wis., 1975), pp. 143–189.
  • D. Bleichenbacher (1996) Efficiency and Security of Cryptosystems Based on Number Theory. Ph.D. Thesis, Swiss Federal Institute of Technology (ETH), Zurich.
  • W. E. Bleick and P. C. C. Wang (1974) Asymptotics of Stirling numbers of the second kind. Proc. Amer. Math. Soc. 42 (2), pp. 575–580.
  • D. Bressoud and S. Wagon (2000) A Course in Computational Number Theory. Key College Publishing, Emeryville, CA.
  • 6: Bibliography C
  • L. Carlitz (1953) Some congruences for the Bernoulli numbers. Amer. J. Math. 75 (1), pp. 163–172.
  • L. Carlitz (1954a) q -Bernoulli and Eulerian numbers. Trans. Amer. Math. Soc. 76 (2), pp. 332–350.
  • L. Carlitz (1954b) A note on Euler numbers and polynomials. Nagoya Math. J. 7, pp. 35–43.
  • L. Carlitz (1958) Expansions of q -Bernoulli numbers. Duke Math. J. 25 (2), pp. 355–364.
  • A. Cayley (1895) An Elementary Treatise on Elliptic Functions. George Bell and Sons, London.