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Physical Mathematics by Kevin Cahill

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2

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Fourier series

2.1 Complex Fourier series

The phases , one for each integer n, are orthonormal on an interval of length 2π

image

(2.1)

where δn,m = 1 if n = m, and δn,m = 0 if nm. So if a function f(x) is a sum of these phases

image

(2.2)

then their orthonormality (2.1) gives the nth coefficient fn as the integral

(2.3)

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