Fourier's Theorem/Lemma 1/Mistake 1

Source Work

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

Mistake

$\ds \int^b \map \psi u \sin N u \rd u = \sum_{r \mathop = 0}^{m - 1} \int_{a_r}^{a_{r + 1} } \map \psi u \sin N u \rd u$

The lower limit is missing from the integral.

It should be:

$\ds \int_a^b \map \psi u \sin N u \rd u = \sum_{r \mathop = 0}^{m - 1} \int_{a_r}^{a_{r + 1} } \map \psi u \sin N u \rd u$

Sources

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