Poisson, Dobinski, Rota and coherent states
New q- Dobinski formula might also be interpreted as the average of specific q-powers of random variable X with the usual Poisson distribution.
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arXiv subjects
A. K. Kwasniewski
Publications and source records attributed to A. K. Kwasniewski.
q-Poisson, q-Dobinski, q-Rota and q-coherent states
q- Dobinski formula may be interpreted as the average of powers of a random variable X_q with the q- Poisson distribution.
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On duality triads
We introduce a duality triads` notion. These are dual recurrences as used in dynamical data bases theory completed by a third pertinacious relation. Several representative examples of them are given. q-Gaussian triads as well as Fibonomial triangle and duality triads in finite operator calculus are presented in the paper that follows this one .
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Towards psi-extension of Rota`s Finite Operator Calculus
A class of extended umbral calculi in operator form is presented. Extensions of all basic theorems of classical Finite Operator Calculus are shown to hold. The impossibility of straightforward extending of quantum q-plane formulation of the q-umbral caculus to the general psi-calculus case is demonstrated.
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On trigonometric-like decompositions of functions with respect to the cyclic group of order n
The cyclic group labeled family of quasi-projection operators is used 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.
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On extended umbral calculus, oscillator-like algebras and Generalized Clifford Algebra
Some quantum algebras build from deformed oscillator algebras may be described in terms of a particular case of extended umbral calculus. We give here an example of a specific relation between such certain quantum algebras and generalized Clifford algebras also in the context of azimuthal quantization of angular momentum which was interpreted afterwards as the finite dimensional quantum mechanics .
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Bernoulli-Taylor formula for psi-umbral difference calculus
An expansion formula of a new type with the rest term of Cauchy type is derived in the operator formulation of generalized umbral calculus
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On Simple Characterisations of Sheffer psi- polynomials and Related Propositions of the Calculus of Sequences
A calculus of sequences started in 1936 opened the way for future extensions of umbral calculus in its finite operator form. Because of historically established notation we call it the psi-calculus.It appears in parts to be almost automatic extension of the standard classical finite operator calculus.
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