q-Stirling numbers

Thomas Ernst
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Thomas Ernst: Uppsala University, Department of Mathematics

Chapter Chapter 5 in A Comprehensive Treatment of q-Calculus, 2012, pp 169-193 from Springer

Abstract: Abstract In this chapter we focus on functions of q x , 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.

Keywords: Difference Operator; Formal Power Series; Orthogonality Relation; Previous Chapter; Bernoulli Polynomial (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/978-3-0348-0431-8_5

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