Proving \int ^{2\pi} _{0} (\cos(t)^{2n})={2n \choose {n}}\frac{2\pi}{2^{2n}}using the following result\int

Seamus Kent 2022-01-26 Answered
Proving 02π(cos(t)2n)=(2nn)2π22n using the following result γ(z+1z)2ndzz=(2nn)2πi Prove 02π(cos(t)2n)=(2nn)2π22n
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Deegan Mullen
Answered 2022-01-27 Author has 12 answers
Take γ={(x,y)|x2+y2=1}. Then γ(z+1/z)2n(1/z)dz=02π(2cost)2n(costisint)(sint+icost)dt=i02π(2cost)2ndt=(2nn)2πi And the rest follows.
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