Exponential operators, quasi-monomials and generalized polynomials

It is shown that the combination of exponential operator techniques and the use of the principle of quasimonomiality can be a very useful tool for a more general insight into the theory of ordinary polynomials and for their extension. We prove the link between Laguerre polynomials and Tricomi functions and study the properties of new classes of polynomials constructed in terms of quasi-monomials. The usefulness of the obtained results to treat radiation physics problems such as wave propagation and quantum beam life-time in storage rings is also discussed. (author)