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On sums of certain trigonometric series

Published online by Cambridge University Press:  17 April 2009

Minking Eie  and
Yao Lin Ong
Minking Eie
Affiliation:
Department of Mathematics, National Chung Cheng University, Ming-Hsiung, Chia-Yi 621, Taiwan, Republic of China, e-mail: mkeie@math.ccu.edu.tw, ylong@alumni.ccu.edu.tw
Yao Lin Ong
Affiliation:
Department of Mathematics, National Chung Cheng University, Ming-Hsiung, Chia-Yi 621, Taiwan, Republic of China, e-mail: mkeie@math.ccu.edu.tw, ylong@alumni.ccu.edu.tw
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Abstract

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Let N be a fixed positive integer. In this paper, we apply a newly developed method of Eie and Lai to the evaluation of certain infinite trigonometric series. Indeed, we are able to express the sums of these series in terms of Bernoulli polynomials. That is, we obtain several new Bernoulli identities. A similar method leads to Ramanujan's identities.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 67 , Issue 1 , February 2003 , pp. 103 - 114
Copyright
Copyright © Australian Mathematical Society 2003

References

REFERENCES

[1]Berndt, B.C., Ramanujan's Notebooks Part I and Part II (Springer-Verlag, Berlin, Heidelberg, New York, 1985 and 1989).Google Scholar
[2]Eie, M. and Lai, K.F., ‘On Bernoulli identities and applications, Part I and II’, Rev. Met. Iberoamericana 14 (1998), 167–213.Google Scholar