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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Computation of tangent, Euler, and Bernoulli numbers


Authors: Donald E. Knuth and Thomas J. Buckholtz
Journal: Math. Comp. 21 (1967), 663-688
MSC: Primary 65.25
MathSciNet review: 0221735
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Abstract | References | Similar Articles | Additional Information

Abstract: Some elementary methods are described which may be used to calculate tangent numbers, Euler numbers, and Bernoulli numbers much more easily and rapidly on electronic computers than the traditional recurrence relations which have been used for over a century. These methods have been used to prepare an accompanying table which extends the existing tables of these numbers. Some theorems about the periodicity of the tangent numbers, which were suggested by the tables, are also proved.


References [Enhancements On Off] (What's this?)

  • [1] Thomas Clausen, "Theorem," Astr. Nachrichten, v. 17, 1840, cols. 351-352.
  • [2] S. A. Joffe, "Calculation of the first thirty-two Eulerian numbers from central differences of zero," Quart. J. Math., v. 47, 1916, pp. 103-126.
  • [3] S. A. Joffe, "Calculation of eighteen more, fifty in all, Eulerian numbers from central differences of zero," Quart. J. Math., v. 48, 1917-1920, pp. 193-271.
  • [4] D. H. Lehmer, An extension of the table of Bernoulli numbers, Duke Math. J. 2 (1936), no. 3, 460–464. MR 1545938, http://dx.doi.org/10.1215/S0012-7094-36-00238-7
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  • [7] S. Z. Serebrennikoff, "Tables des premiers quatre vingt dix nombres de Bernoulli," Mém. Acad. St. Petersbourg 8, v. 16, 1905, no. 10, pp. 1-8.
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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1967-0221735-9
PII: S 0025-5718(1967)0221735-9
Article copyright: © Copyright 1967 American Mathematical Society