Generalized Q-Exponentials Related to Orthogonal Quantum Groups and Fourier Transformations of Noncommutative Spaces

An essential prerequisite for the study of q-deformed physics are particle states in position and momentum representation. In order to relate x- and p-space by Fourier transformations the appropriate q-exponential series related to orthogonal quantum symmetries is constructed. It turns out to be a new q-special function giving rise to q-plane wave solutions that transform with a noncommuting phase under translations.