D-polynomials and Taylor formula in quantum calculus

Details D-polynomials and Taylor formula in quantum calculus D-polynomials and Taylor formula in quantum calculus

2010-12-13

arxiv.org/abs/1012.2611v2

Mathematics

Quantum Algebra

Scientific paper

Quantum calculus based on the right invertible divided difference operator $D_{\sigma}^{\tau}$ is proposed here in context of algebraic analysis \cite{DPR}. The linear operator $D_{\sigma}^{\tau}$, specified with the help of two fixed maps $\sigma\;, \tau\colon M\rightarrow M$, generalizes the quantum derivative operator used in $h$- or $q$-calculus \cite{kac}. In the domain of $D_{\sigma}^{\tau}$ there are special elements defined as $D_{\sigma}^{\tau}$-polynomials and the corresponding Taylor formula is proved.

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