# A Comprehensive Treatment of q-Calculusq-Stirling numbers

A Comprehensive Treatment of q-Calculus: q-Stirling numbers [In this chapter we focus on functions of qx, or equivalently functions of the q-binomial coefficients. We systematically find q-analogues of the formulas for Stirling numbers from Jordan and the elementary textbooks by J. Cigler and Schwatt. To this end, various q-difference operators are used. In each of Sections 5.2–5.4, we focus on a certain such △q operator and find four formulas (the quartet of formulas) in each section. A q-power sum of Carlitz plays a special role. We present tables and recurrence formulas for the two polynomial q-Stirling numbers.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

# A Comprehensive Treatment of q-Calculusq-Stirling numbers

24 pages

/lp/springer-journals/a-comprehensive-treatment-of-q-calculus-q-stirling-numbers-l2pIEnwM6l
Publisher
Springer Basel
ISBN
978-3-0348-0430-1
Pages
169 –193
DOI
10.1007/978-3-0348-0431-8_5
Publisher site
See Chapter on Publisher Site

### Abstract

[In this chapter we focus on functions of qx, or equivalently functions of the q-binomial coefficients. We systematically find q-analogues of the formulas for Stirling numbers from Jordan and the elementary textbooks by J. Cigler and Schwatt. To this end, various q-difference operators are used. In each of Sections 5.2–5.4, we focus on a certain such △q operator and find four formulas (the quartet of formulas) in each section. A q-power sum of Carlitz plays a special role. We present tables and recurrence formulas for the two polynomial q-Stirling numbers.]

Published: Jun 18, 2012

Keywords: Difference Operator; Formal Power Series; Orthogonality Relation; Previous Chapter; Bernoulli Polynomial