A rapidly convergent series for \(\log N!\). (Q1470521)
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scientific article; zbMATH DE number 2610669
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A rapidly convergent series for \(\log N!\). |
scientific article; zbMATH DE number 2610669 |
Statements
A rapidly convergent series for \(\log N!\). (English)
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1917
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Elementare Herleitung der Formel \[ \log N!=(N+\frac 12)\log(N+\frac 12)-N+C-\sum_{r=1}^\infty \sum_{n=N+1}^\infty \frac{1}{2r(2r+1)2^{2r}n^{2r}}, \] die zur angenäherten Berechnung von \(N!\) geeignet ist. Man hat hierbei \[ C=\log\sqrt{\frac{2\pi}{e}}=0,418938\dots \]
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