  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.
