AbstractThe interrelationship between distinct umbral calculi is studied. These ideas are applied in particular to q-umbral calculus, which shows how Andrews' q-theory relates to the q-theory discussed in the previous paper by the author. The q-Hermite polynomials and basic hypergeometric series are briefly discussed
The use of non-standard calculus means have been proven to be extremely powerful for studying old an...
The aim of this paper is to develop foundations of umbral calculus on the space $\mathcal D'$ of di...
In the spirit of our earlier articles on \(q\)-\(\omega\) special functions, the purpose of this art...
AbstractThe interrelationship between distinct umbral calculi is studied. These ideas are applied in...
AbstractAn algebraic setting for the Roman-Rota umbral calculus is introduced. It is shown how many ...
We present a variety of q-formulas linked together by the q-umbral calculus introduced here, equival...
summary:This paper deals with $\varphi(q)$ calculus which is an extension of finite operator calculu...
Following the approach of Rota and Taylor, we present an innovative theory of Sheffer sequences in w...
AbstractRota's Umbral Calculus uses sequences of Sheffer polynomials to count certain combinatorial ...
The q-calculus is reformulated in terms of the umbral calculus and of the associated operational for...
AbstractWe introduce natural q-analogs of hypergeometric series well-poised in SU(n), the related hy...
The present note envisage to derive some new classes of multiple q-series transformations and reduct...
summary:The paper deals with extensions of the finite operator calculus of G.-C. Rota called $\psi$-...
AbstractThe partial difference equation r(i, j) = r(i, j − 1) + r(i − 1, j) + r(i − 1, J + 1), where...
AbstractAs an application of the transformation theory of basic (or q-) hypergeometric series, a num...
The use of non-standard calculus means have been proven to be extremely powerful for studying old an...
The aim of this paper is to develop foundations of umbral calculus on the space $\mathcal D'$ of di...
In the spirit of our earlier articles on \(q\)-\(\omega\) special functions, the purpose of this art...
AbstractThe interrelationship between distinct umbral calculi is studied. These ideas are applied in...
AbstractAn algebraic setting for the Roman-Rota umbral calculus is introduced. It is shown how many ...
We present a variety of q-formulas linked together by the q-umbral calculus introduced here, equival...
summary:This paper deals with $\varphi(q)$ calculus which is an extension of finite operator calculu...
Following the approach of Rota and Taylor, we present an innovative theory of Sheffer sequences in w...
AbstractRota's Umbral Calculus uses sequences of Sheffer polynomials to count certain combinatorial ...
The q-calculus is reformulated in terms of the umbral calculus and of the associated operational for...
AbstractWe introduce natural q-analogs of hypergeometric series well-poised in SU(n), the related hy...
The present note envisage to derive some new classes of multiple q-series transformations and reduct...
summary:The paper deals with extensions of the finite operator calculus of G.-C. Rota called $\psi$-...
AbstractThe partial difference equation r(i, j) = r(i, j − 1) + r(i − 1, j) + r(i − 1, J + 1), where...
AbstractAs an application of the transformation theory of basic (or q-) hypergeometric series, a num...
The use of non-standard calculus means have been proven to be extremely powerful for studying old an...
The aim of this paper is to develop foundations of umbral calculus on the space $\mathcal D'$ of di...
In the spirit of our earlier articles on \(q\)-\(\omega\) special functions, the purpose of this art...
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