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$$\begin{eqnarray*} f(x) & = & \sum_{k=0}^{n-1} \frac{f^{(k)}(a)}{k!}(x-a)^k + O(... ...+ \cdots + \frac{f^{(n-1)}(a)}{(n-1)!}(x-a)^{n-1} + O((x-a)^n) \end{eqnarray*}$$

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$$f(t)=\cos(at)\mathop{\rm sech}(bt)$$

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