Q-Analogues of Symbolic Operators. (14th July 2013) - Dancs, Michael J.; He, Tian-Xiao
Abstract : 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 He et al., 2007, 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.