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Find Z-transform of {k2 - 2k + 3}k ≥ 0
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We assume

([f(k)]=0 \ for \ k \ < 0)

Here, $f(k)=k^2-2k+3, \ By\ definition,$

$Z[f(k)]=\sum_{k=-\infty}^{\infty} f(k).z^{-k}$

$Z[k^2-2k+3]$

$=\sum_{k=-\infty}^{-1}0+\sum_{k=0}^{\infty}(k^2-2k+3)\dfrac {1}{z^k}$

$=\dfrac {3} {z^0}+\dfrac {2} {z^1}+\dfrac {3} {z^2}+ \dfrac {6} {z^3}+\dfrac {11} {z^4}+...$

$=3+\dfrac {2} {z}+\dfrac {3} {z^2}+ \dfrac {6} {z^3}+\dfrac {11} {z^4}+...$

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