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Sinc function

1 byte added, 18:48, 19 December 2011
Higher derivative at zero
The limit procedure used for the first and second derivatives can be extended to the computation of higher derivatives at zero. However, this process is tedious. An alternative approach is to use the [[power series]] expansion:
<math>\operatorname{sinc} x = 1 - \frac{x^2}{3!} + \frac{x^4}{5!} - \dots = \sum_{k=0}^\infty \frac{(-1)^kx^{2k}}{(2k + 1)!}</math>
Since this is a power series, it is also a Taylor series. Thus, the coefficient of <math>x^{2k}</math> is <math>1/(2k)!</math> times <math>\operatorname{sinc}^{(2k)}(0)</math>. We thus get:

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