How does one show that $I_n=\int\limits_0^1 (1-x^2)^ndx $ satisfies the recursion relation $I_n={2n\over 2n+1}I_{n-1}$? I don't think I have to explicitly evaluate the integral right?
Thanks.
How does one show that $I_n=\int\limits_0^1 (1-x^2)^ndx $ satisfies the recursion relation $I_n={2n\over 2n+1}I_{n-1}$? I don't think I have to explicitly evaluate the integral right?
Thanks.