I know that if $\mathcal{F}$ is the Fourier transform then $\mathcal{F}\Big\{f(x-x_0)\Big\}=\exp{\{2ix_0\zeta}\}\mathcal{F}\Big\{f\Big\}(\zeta)$. I am so confused, is there any relation from this statement to derive $\mathcal{F}\Bigg\{\Big(f(x-x_0)+f(x-x_1)\Big)^{n}\Bigg\}$? where $n$ is an even integer. I tried to derive this from a previous asked question: Fourier Transform of $|x|^n$ without any success.
2026-03-28 17:41:49.1774719709
Fourier transform of sum to the power n
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