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On the Fourier coefficients of a discontinuous function
Published online by Cambridge University Press: 20 January 2009
Extract
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
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