The deformed double covering of E(2) group, denoted by $\tilde{ E}_\kappa(2)$, is obtained by contraction from the $SU_\mu(2)$. The contraction procedure is then used for producing a new examples of differential calculi: 3D-left covariant calculus on both $\tilde{ E}_\kappa(2)$ and the deformed Euclidean group $E_\kappa(2)$ and two different 4D-bicovariant calculi on $\tilde{ E}_\kappa(2)$ which correspond to the one 4D-bicovariant calculi on $E_\kappa(2)$ described in Ref.\cite{ b14}.
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