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About LinkBacksWhy is this?Originally Posted by ThePerfectHacker
If you have a power series and the termsare sufficiently bounded, say,
then the series converges absolutely on
and so it is okay to differenciate term-by-term.
Ifconverges on
for some
then this function is
on this open interval i.e. infinitely differenciable and the derivative is given by term-by-term differenciation. This is just a result from analysis.
Ifare too huge then
but if they are bounded big enough then there will be an an interval centered at
on which it converges.
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