3. Examine the proof of Bessel’s inequality and show that equality holds if the Fourier series of…

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3.    Examine the proof of Bessel’s inequality and show that equality holds if the Fourier series of ϕ converges to ϕ uniformly. This is known as Parseval’s equality. Apply Par- seval’s equality to the Fourier series in Example 6.4.3 to derive the summation identity

∞      1        π4

 

n=1

n4  = 90 .