Note on Binet's inverse factorial series for \(\mu (x)\). (Q1453406)
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scientific article; zbMATH DE number 2591771
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Note on Binet's inverse factorial series for \(\mu (x)\). |
scientific article; zbMATH DE number 2591771 |
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Note on Binet's inverse factorial series for \(\mu (x)\). (English)
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1925
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Neue Herleitung [der \textit{Binet}schen Entwicklung (Journ. Ecole Polytechnique 16 (1839), 123-343) \[ \begin{aligned} \log \varGamma(x) - &(x - \frac 12) \log x + x - \frac 12 \log 2\pi\\ &= \sum_{n=1}^\infty \frac {[x]^{-n}}{2n} \int_0^1(a + 1)(a+2)\ldots (a+ n -1)(2a-1)\,a\,da, \end{aligned} \] wo \([x]^n\) erklärt ist als \(\dfrac{\varGamma(1+x)}{\varGamma(1+x-n)}\).
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