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

Seamus Kent

Seamus Kent

Answered question

2022-01-26

Proving 02π(cos(t)2n)=(2nn)2π22n using the following result γ(z+1z)2ndzz=(2nn)2πi Prove 02π(cos(t)2n)=(2nn)2π22n

Answer & Explanation

Deegan Mullen

Deegan Mullen

Beginner2022-01-27Added 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.

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?