On the Fourier coefficients of a discontinuous function
1941 ◽
Vol 6
(4)
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pp. 231-256
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We suppose throughout that f(t) is periodic with period 2π, and Lebesgue-integrable in (− π, π).We writeand 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).
1973 ◽
Vol 16
(1)
◽
pp. 93-103
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1967 ◽
Vol 63
(3)
◽
pp. 703-705
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Keyword(s):
1924 ◽
Vol 106
(737)
◽
pp. 299-314
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2015 ◽
Vol 58
(4)
◽
pp. 858-868
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1968 ◽
Vol 64
(1)
◽
pp. 61-66
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Keyword(s):