Q-analogues of Symbolic Operators

Authors

Tian-Xiao He, Illinois Wesleyan UniversityFollow
Michael Dancs

Publication Date

January 2013

Comments

The Journal of Discrete Mathematics is published by the Hindawi Publishing Corporation, http://www.hindawi.com/.

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.

Disciplines

Mathematics

Recommended Citation

He, Tian-Xiao and Dancs, Michael, "Q-analogues of Symbolic Operators" (2013). Scholarship. 7.
https://digitalcommons.iwu.edu/math_scholarship/7