Whenever we get a break from working with clients, we like to help people with their matthematics and statistics problem on Reddit. The following problem was one that was posed this past weekend on Reddit.
Define iteratively as follows , and for The problem is to evaluate
To evaluate the integral, the substitution is made. With defined by
one has The advantage conferred by this substitution is that the functions take on much simplier form that the functions .
Note that and for It follows that and At this point the pattern is clear, and induction can be used to prove that for A straightforward integration yields