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On the Fourier coefficients of a discontinuous function

Published online by Cambridge University Press:  20 January 2009

S. P. Bhatnagar
S. P. Bhatnagar
Affiliation:
University College, London.
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We suppose throughout that f(t) is periodic with period 2π, and Lebesgue-integrable in (− π, π).

We write

and suppose that the Fourier series of φ(t) and ψ(t) are respectively cos nt and sin nt. Then the Fourier series and allied series of f(t) at the point t = x are respectively and , where A0 = ½a0, An = ancos nx + bnsin nx, Bn = bncos nx − ansin nx and an, bn are the Fourier coefficients of f(t).

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 6 , Issue 4 , October 1941 , pp. 231 - 256
Copyright
Copyright © Edinburgh Mathematical Society 1941

References

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