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A RECURRENCE RELATION FOR BERNOULLI NUMBERS

  • CAN MUMUN ;
  • CENKCI MEHMET ;
  • KURT VELI
  • Published : 2005.08.01

Abstract

In this paper, using Gauss multiplication formula, a recurrence relation for Bernoulli numbers, generalizing Namias' results, is given.

Keywords

Bernoulli numbers;Stirling's series;Gauss multiplication formula

References

  1. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, National Bureu of Standarts, Appl. Math. Series 55 (1965)
  2. T. M. Apostol, Introduction to Analytic Number Theory, Springer-Verlag, 1985
  3. E. Y. Deeba and D. M. Rodriguez, Stirling's Series and Bernoulli Numbers, Amer. Math. Monthly 98 (1991), 423-426 https://doi.org/10.2307/2323860
  4. F. T. Howard, Applications of a Recurrence for the Bernoulli Numbers, J. Number Theory 52 (1995), 157-172 https://doi.org/10.1006/jnth.1995.1062
  5. V. Namias, A Simple Derivation of Stirling's Asymptotic Series, Amer. Math. Monthly 93 (1986), 25-29 https://doi.org/10.2307/2322540