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Further remarks on extended umbral calculus. (English) Zbl 1018.05008
Slovák, Jan (ed.) et al., The proceedings of the 21th winter school “Geometry and physics”, Srní, Czech Republic, January 13-20, 2001. Palermo: Circolo Matemàtico di Palermo, Suppl. Rend. Circ. Mat. Palermo, II. Ser. 69, 117-130 (2002).
The paper deals with extensions of the finite operator calculus of G.-C. Rota called $$\psi$$-extensions which give a framework for corresponding quantum group investigations. This also covers the instance of the well-known $$q$$-analogue of umbral calculus. The article also contains glossaries of the most important terms and notations used by Ward, Viskov, Markowsky and Roman on one side and the Rota-oriented notations on the other side.
For the entire collection see [Zbl 0994.00029].

##### MSC:
 05A40 Umbral calculus 81S99 General quantum mechanics and problems of quantization
##### Keywords:
umbral calculus; finite operator calculus