量子微积分中的D-多项式与泰勒公式
D-polynomials and Taylor formula in quantum calculus
摘要：
本文在代数分析\cite{DPR}的背景下提出了基于右可逆均差算子$D_σ^τ$的量子演算。借助于两个固定映射$σ\;, τ\colon M\rightarrow M$指定的线性算子$D_σ^τ$推广了在$h$ -或$q$ -演算\cite{kac}中使用的量子导数算子。在$D_σ^τ$的定义域中，定义了$D_σ^τ$ -多项式的特殊元素，并证明了相应的泰勒公式.
英文摘要：
Quantum calculus based on the right invertible divided difference operator $D_σ^τ$ is proposed here in context of algebraic analysis \cite{DPR}. The linear operator $D_σ^τ$, specified with the help of two fixed maps $σ\;, τ\colon M\rightarrow M$, generalizes the quantum derivative operator used in $h$- or $q$-calculus \cite{kac}. In the domain of $D_σ^τ$ there are special elements defined as $D_σ^τ$-polynomials and the corresponding Taylor formula is proved.
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