Question Number 103314 by Ar Brandon last updated on 14/Jul/20

Linearise cos^(2(p−1)) (t)

Answered by OlafThorendsen last updated on 14/Jul/20

cos^(2(p−1)) (t) = [((e^(it) +e^(−it) )/2)]^(2(p−1)) cos^(2(p−1)) (t) = (1/4^(p−1) )Σ_(k=0) ^(2(p−1)) C_(2(p−1)) ^k e^(ikt) e^(−it(2p−2−k)) cos^(2(p−1)) (t) = (1/4^(p−1) )Σ_(k=0) ^(2(p−1)) C_(2(p−1)) ^k e^(−it(2p−2−2k)) cos^(2(p−1)) (t) = (1/4^(p−1) )Σ_(k=0) ^(2(p−1)) C_(2(p−1)) ^k e^(2it(k+1−p)) cos^(2(p−1)) (t) = (((2p−2)!)/4^(p−1) )Σ_(k=0) ^(2(p−1)) ((cos[2(k+1−p)t])/(k!(2p−2−k)!))

Commented byAr Brandon last updated on 14/Jul/20

Thanks