Fourier's Theorem/Lemma 1/Mistake 2

Source Work

  • 1961: I.N. Sneddon: Fourier Series:Chapter Two: $\S 2$. Some Important Limits


Mistake

... If $M$ is the greatest of the finite numbers $1 M_0 1, 1 M_1 1, \ldots, 1 M_{m - 1} 1$ we have
$\ds 1 \int_a^b \map \psi u \sin N u \rd u 1 < \dfrac {M m} N$


This appears to be an error of transcription from the manuscript to the typeset copy, where absolute value indicators have been interpreted as instances of the number $1$.


This should read:

... If $M$ is the greatest of the finite numbers $\size {M_0}, \size {M_1}, \ldots, \size {M_{m - 1} }$ we have
$\ds \size {\int_a^b \map \psi u \sin N u \rd u} < \dfrac {M m} N$


Sources

  • 1961: I.N. Sneddon: Fourier Series ... (previous) ... (next): Chapter Two: $\S 2$. Some Important Limits
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