On trigonometric-like decompositions of functions with respect to the cyclic group of order n

The cyclic group labelled family of α-projection operators implicitly present in [28] is used as in [5]-[9], [23] for investigation of decomposition of functions with respect to the cyclic group of order n. Series of new identities thus arising are demonstrated and new perspectives for further investigation are indicated as for example in the case of q-extended special polynomials. The paper constitutes an example of the application of the method of projections introduced in [26]; see also references [5]-[9].