Q-Analogues of Symbolic Operators

Abstract EN

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.