A note on Bernoulli numbers

Ramesh Kumar Muthumalai
Notes on Number Theory and Discrete Mathematics, ISSN 1310–5132
Volume 19, 2013, Number 1, Pages 59–65
Full paper (PDF, 139 Kb)

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Authors and affiliations

Ramesh Kumar Muthumalai
Department of Mathematics, D.G. Vaishnav College
Chennai-600106, Tamil Nadu, India

Abstract

Some explicit formulae for Bernoulli numbers and Bernoulli polynomials are derived. Some rational approimations to powers of π are given in terms of Bernoulli numbers.

Keywords

• Bernoulli numbers
• Bernoulli polynomials
• Stirling numbers
• Identities
• π

AMS Classification

• 11B68

References

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2. Gradshteyn, I. S., I. M. Ryzhik, Tables of Integrals, Series and Products, 6th Edition, Academic Press, USA, 2000.
3. Ireland, K., M. Rosen, A Classical Introduction to Modern Number Theory, 2nd Edition, Springer-verlag, New York, 1990.
4. Muthumalai, R. K. Some properties and applications of generalized Bernoulli polynomials, Int. Jour. Appl. Math., Vol. 25, 2012, No. 1, 83–93.
5. Sándor, J., B. Crstici, Handbook of Number Theory II, Springer, Kluwer Acedemic Publishers, The Netherlands, 2004.