A Newton interpolation approach to generalized Stirling numbers (Q410940)
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scientific article; zbMATH DE number 6021674
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A Newton interpolation approach to generalized Stirling numbers |
scientific article; zbMATH DE number 6021674 |
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A Newton interpolation approach to generalized Stirling numbers (English)
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4 April 2012
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Summary: We employ the generalized factorials to define a Stirling-type pair \(\{s(n, k; \mathbf{\alpha, \beta}, r), S(n, k; \mathbf{\alpha, \beta}, r)\}\) which unifies various Stirling-type numbers investigated by previous authors. We make use of the Newton interpolation and divided differences to obtain some basic properties of the generalized Stirling numbers including the recurrence relation, explicit expression, and generating function. The generalizations of the well-known Dobinski's formula are further investigated.
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0.9217526
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0.9109526
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0.89442533
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0.8886164
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0.88763183
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