Its been while since I asked a question... So here goes nothing!
This is from "Baby Rudin." Pg. 199, #12, (d).
Using:
δ→0limn≥1∑n2δsin2(nδ)=2π
How to show:
∫0∞(xsinx)2dx=2π
Parts (a),(b),(c) have been proven. They are quoted here:
Thanks!
This is from "Baby Rudin." Pg. 199, #12, (d).
Using:
δ→0limn≥1∑n2δsin2(nδ)=2π
How to show:
∫0∞(xsinx)2dx=2π
Parts (a),(b),(c) have been proven. They are quoted here:
Part a: Compute the Fourier coefficients of f.
f(x)=0 when δ<∣x∣≤π and f(x)=1 when ∣x∣≤δ.
f(x+2π)=f(x)∀x, 0<δ<π
Part b: Show
n≥1∑nsinnδ=2π−δ
Part c: Show, using Parseval's Thm:
n≥1∑n2δ(sinnδ)2=2π−δ
Thanks!