On certain summation problems and generalizations of Eulerian polynomials and numbers (Q1300978)
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scientific article; zbMATH DE number 1331475
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On certain summation problems and generalizations of Eulerian polynomials and numbers |
scientific article; zbMATH DE number 1331475 |
Statements
On certain summation problems and generalizations of Eulerian polynomials and numbers (English)
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14 June 2000
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The authors introduce two kinds of generalized Euler polynomials and numbers in order to obtain close summations formulae for extended arithmetic-geometric series. By using elementary combinatorial analysis, some basic formulas for Carlitz-Howard's degenerated numbers, as well as Dickson-Stirling numbers are deduced. For the interested reader we quote the papers by \textit{L. Carlitz} [Utilitas Math. 15, 51-88 (1978; Zbl 0404.05004)], \textit{F. T. Howard} [Discrete Math. 57, 45-58 (1985; Zbl 0606.10009)] as well as the book by \textit{R. Lidl, G. L. Mullen} and \textit{G. Turnwald} [Dickson polynomials, Pitman Monographs and Surveys, Pure Appl. Math. 65 (1993; Zbl 0823.11070)].
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generalized Euler number
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Dickson-Euler numbers
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generalized Euler polynomials
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Dickson-Stirling numbers
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