Definition talk:Fourier Series/Formulation 2

Overcomplicated?

I have a feeling that this can also be expressed as:

\(\ds A_m\)

\(=\)

\(\ds \dfrac 2 {b - a} \int_a^b \map f x \cos \frac {2 m \pi x} {b - a} \rd x\)

\(\ds B_m\)

\(=\)

\(\ds \dfrac 2 {b - a} \int_a^b \map f x \sin \frac {2 m \pi x} {b - a} \rd x\)

where:

$\ds \frac {A_0} 2 + \sum_{m \mathop = 1}^\infty \paren {A_m \cos \frac {2 m \pi x} {b - a} + B_m \sin \frac {2 m \pi x} {b - a} }$

because it is immaterial what range of length $2 \pi$ you use -- as both sine and cosine spend as much time over the $x$-axis as under it, it all works out the same.

A second pair of eyes and a rigorous organisational ability is needed to knock this section on Fourier series into proper shape. --prime mover (talk) 02:03, 8 March 2018 (EST)