Assume that f has a Fourier sine seriesf(x) = n=1bn
Chapter 10, Problem 37(choose chapter or problem)
Assume that f has a Fourier sine seriesf(x) = n=1bn sin(nx/L), 0 x L.(a) Show formally that2LL0[f(x)]2 dx = n=1b2n.Compare this result (Parsevals equation) with that of in Section 10.3. Whatis the corresponding result if f has a cosine series?(b) Apply the result of part (a) to the series for the sawtooth wave given in Eq. (9), andthereby show that26 = 1 +122 +132 += n=11n2 .This relation was discovered by Euler in about 1735.
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