Let be infinitely differentiable and suppose that
for all . Determine the values of.
Since , it follows that one such function would be . Comparing that with the Taylor series , you see that for this particular function if n is odd, and .
That tells you what you should expect the answer to be, but of course it isn't a proof. To set about proving the result, you will have to use techniques like those in Drexel28's comment. But knowing what to expect the answer to be can sometimes be a help in establishing it.