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Author Ernst, Thomas
Source CiteSeerX
Content type Text
File Format PDF
Language English
Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science
Subject Keyword Q-stirling Number ♦ Q-binomial Coefficient Identity ♦ Multiple Sum ♦ Q-difference Operator ♦ Umbral Approach ♦ Carlitz Gould ♦ Different Formula ♦ Different Approach ♦ First One ♦ Hahn Cigler ♦ Respective Q-taylor Formula ♦ Basic Formula ♦ Third Approach ♦ Carlitz Q-analogue ♦ Q-binomial Coefficient ♦ Double Sum
Description Three different approaches to q-difference operators are given, the first one applies to C(q)[x] and the last two to C(q)[q x]. For the first one (Hahn–Cigler), definitions and basic formulas for the two q-Stirling numbers are given. For the second (Carlitz–Gould), and third approach (Jackson), the respective q-Taylor formulas are used to find a q-binomial coefficient identity. Three different formulas for Carlitz ’ q-analogue of sums of powers are found. The first one uses a double sum for q-Stirling numbers. The last two are multiple sums with q-binomial coefficients.
Educational Role Student ♦ Teacher
Age Range above 22 year
Educational Use Research
Education Level UG and PG ♦ Career/Technical Study
Learning Resource Type Article
Publisher Institution Advances in Dynamical Systems and Applications