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

?