Let us consider a periodic single valued function *f*(*x*) in the interval *–π ≤ x ≤ π* [such that *f*(*x +* 2*π*) **=*** f*(*x*)]. The Fourier series corresponding to *f*(*x*) is defined as

This series converges in the said interval (*–π, π*)*,* if *f*(*x*) and *f′*(*x*) [= (*∂f /∂x*)] are continuous. Multiplying Eq. (B.1) by cos(*mx*) and integrating over –*π* to *π,* we get

Again multiplying (B.1) by sin (*mx*) and integrating over −*π* to *π,* we get

The series (B.1) may also be written in an alternative form ...

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