Let be infinitely differentiable and suppose that

for all . Determine the values of.

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- Jan 20th 2011, 08:20 AMMarkeurValues of derivatives
Let be infinitely differentiable and suppose that

for all . Determine the values of. - Jan 20th 2011, 04:29 PMDrexel28
- Jan 21st 2011, 01:33 AMOpalg
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.