Hostname: page-component-76fb5796d-wq484 Total loading time: 0 Render date: 2024-04-26T22:53:34.536Z Has data issue: false hasContentIssue false
  • English
  • Français

On recurrence relations for Bernoulli and Euler numbers

Published online by Cambridge University Press:  17 April 2009

Ching-Hua Chang  and
Chung-Wei Ha
Ching-Hua Chang
Affiliation:
Department of Mathematics, Hualien Teachers College, Hualien, Taiwa e-mail: chchang@sparc2.nhltc.edu.tw
Chung-Wei Ha
Affiliation:
Department of Mathematics, Tsing Hua University, Hsinchu, Taiwan e-mail: cwha@math.nthu.eud.tw
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We obtain a class of recurrence relations for the Bernoulli numbers that includes a recurrence formula proved recently by M. Kaneko. Analogous formulas are also derived for the Euler and Genocchi numbers.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 64 , Issue 3 , December 2001 , pp. 469 - 474
Copyright
Copyright © Australian Mathematical Society 2001

References

[1]Abramowitz, M. and Stegun, A., Handbook of mathematical functions, Appl. Math. Ser. 55 (National Bureau of Standards, Washington D.C., 1972).Google Scholar
[2]Comtet, L., Advanced combinatorics (Reidel, Dordrecht and Boston, 1974).CrossRefGoogle Scholar
[3]Dilcher, K., ‘Sums and products of Bernoulli numbers’, J. Number Theory 60 (1996), 23–41.CrossRefGoogle Scholar
[4]Horadam, A.F., ‘Genocchi polynomials’, in Applications of Fibonacci numbers, (Bergum, G.E. et al. , Editor) (Kluwer Academic Publishers, Dordrecht, 1991), pp. 145–166.CrossRefGoogle Scholar
[5]Howard, F.T., ‘Applications of a recurrence for the Bernoulli numbers’, J. Number Theory 52 (1995), 157–172.CrossRefGoogle Scholar
[6]Kaneko, M., ‘A recurrence formula for the Bernoulli numbers’, Proc. Japan Acad. Ser. A 71 (1995), 192–193.CrossRefGoogle Scholar
[7]Riordan, J., Combinatorial identities (R.E. Krieger Publishing Co., New York, 1979).Google Scholar
[8]Satoh, J., ‘A recurrence formula for q-Bernoulli numbers attached to formal group’, Nagoya Math. J. 157 (2000), 93–101.CrossRefGoogle Scholar