Trying to find the fourier series of $\cosh(ax)$, where $a$ is any real non-zero number, on $[−\pi, \pi]$. So far i've got $$ f(x) = \frac{\sinh(a\pi)}{a\pi} \sum_{n=1}^\infty \frac{2n\cosh(a\pi)\sin(n\pi)+2a\sinh(a\pi)\cos(n\pi)}{\pi(n^2+a^2)}\cos(nx) $$ Does anyone know if this is correct and if there is any way to simplify?
fourier series of $\cosh(ax)$
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fourier-series
1 Answers
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You can apply the following simplifications $$\sin(\pi n) = 0, \forall n \in \mathbb{N}$$ and $$\cos(\pi n) = (-1)^n, \forall n \in \mathbb{N}.$$ But your result is correct.