Prove the following recursion formula holds:
Apply this formula to find the solution of
Proof. To obtain this recursion formula we proceed by integrating by parts. To that end, let
Then we have
Now, to find the solution of
we apply the formula with . This gives us,
Next we apply the formula to the resulting integral with and . Therefore we have
Finally, we apply the formula to the integral above with and to obtain,
Shouldn’t we assume
?