New summation expressions involving the gamma function (Q1302704)
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scientific article; zbMATH DE number 1341312
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | New summation expressions involving the gamma function |
scientific article; zbMATH DE number 1341312 |
Statements
New summation expressions involving the gamma function (English)
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27 March 2000
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One of the results offered is \[ \sum_{k=0}^{\infty}\frac{k!}{\Gamma(k+\beta+2)}\Biggl(\sum_{m=1}^{k}(1/m)\Biggr)=\beta^{-2} / \Gamma(\beta+1) \] \((\beta\neq 0).\)
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gamma function
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series expansion
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perturbation
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0.89560944
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0.8912749
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0.8835944
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0.88281596
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0.88207376
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