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![[parent]](http://images.planetmath.org:8080/images/uparrow.png) Viewing Correction to 'gamma function'
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On definition by scineram
Correction id: 5521
Filed on: 2005-01-01 21:44:03
Status: Rejected on 2005-03-17 16:46:54
Type: Meta/Minor
Correction text:
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As I know, the integral definition is good for only $\mathcal{R}[z]>0$, because $\int_0^1 e^{-t}t^{z-1}dt$ is not necessarily convergent in the other half-plane. However, for $\mathcal{R}[x]>0$ this integral is equal to $\sum_{n=0}^\infty\frac{(-1)^n}{n!(z+n)}$, so the function can be extended to $\mathbb{C}\setminus\{-\mathbb{N}\}$ as $$\Gamma(z)=\sum_{n=0}^\infty\frac{(-1)^n}{n!(z+n)}+\int\limits_1^\infty e^{-t}t^{z-1}dt.$$ |
Comment from correction handler akrowne:
| filer failed to follow up (see post to original correction) |
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