Integral over 2 pi of Cosine of n x/Mistake
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Source Work
- 1961: I.N. Sneddon: Fourier Series: Chapter One: $\S 2$. Fourier Series: $(4)$
Mistake
- $\ds \int_0^{2 \pi} \cos n x \rd x = 0$
It is implicit that $n$ ranges over all integers.
The author has neglected to specify the case where $n = 0$:
- $\ds \int_0^{2 \pi} \cos n x \rd x = \begin {cases} 0 & : n \ne 0 \\ 2 \pi & : n = 0 \end {cases}$
As it stands, the Fourier coefficient $a_0$ is glossed over.
Sources
- 1961: I.N. Sneddon: Fourier Series ... (previous) ... (next): Chapter One: $\S 2$. Fourier Series: $(4)$