\(Q\)-analogues of symbolic operators (Q2249927)

Summary: Here presented are \(q\)-extensions of several linear operators including a novel \(q\)-analogue of the derivative operator \(D\). Some \(q\)-analogues of the symbolic substitution rules given by \textit{T.-X. He} et al. [Comput. Math. Appl. 54, No. 5, 664--678 (2007; Zbl 1155.65300)], are obtained. As sample applications, we show how these \(q\)-substitution rules may be used to construct symbolic summation and series transformation formulas, including \(q\)-analogues of the classical Euler transformations for accelerating the convergence of alternating series.