## Related questions with answers

Question

Using the Maclaurin series, show that if f(z) is even, its integral (with a suitable constant of integration) is odd.

Solution

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Answered 2 years ago

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1 of 7Assume we are given arbitrary function $f(x)$. Maclaurin series of this function is Taylor series at the point $z_0=0$. In other words, Maclaurin series is the following series:

$\begin{equation*} f(z)=\sum_{n=0}^{\infty}a_nz^n \end{equation*}$

where coefficients $a_n$ are calculated with following formula:

$a_n=\frac{1}{n!}\cdot f^{(n)}(0)$

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