Discrete-time Fourier transform of $a^{|n|} u[n]$
There's an obvious typo in that DTFT pair, because - as you've probably noted yourself - we clearly have $\alpha^{|n|}u[n]=\alpha^nu[n]$.
The given expression for the DTFT corresponds to the two-sided time-domain sequence $\alpha^{|n|}$, if $|\alpha|&lt;1$ holds.