Fourier's Theorem/Lemma 1/Mistake 2

Source Work

 * :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
 * $\displaystyle 1 \int_a^b \psi \left({u}\right) \sin N u \rd u 1 < \dfrac {M m} N$

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 $\left\lvert{M_0}\right\rvert, \left\lvert{M_1}\right\rvert, \ldots, \left\lvert{M_{m - 1} }\right\rvert$ we have
 * $\displaystyle \left\lvert{\int_a^b \psi \left({u}\right) \sin N u \rd u}\right\rvert < \dfrac {M m} N$