Difference between revisions of "Gauss' formula for gamma function"
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(Created page with "==Theorem== The following formula holds for $z \in \mathbb{C} \setminus \{0,-1,-2,\ldots\}$: $$\Gamma(z) = \displaystyle\lim_{n \rightarrow \infty} \dfrac{n! n^z}{z(z+1)\ldots...") |
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| − | * {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev= | + | * {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=Gamma|next=Product representation for reciprocal gamma}}: 6.1.2 |
Latest revision as of 07:03, 8 June 2016
Theorem
The following formula holds for $z \in \mathbb{C} \setminus \{0,-1,-2,\ldots\}$: $$\Gamma(z) = \displaystyle\lim_{n \rightarrow \infty} \dfrac{n! n^z}{z(z+1)\ldots(z+n)},$$ where $\Gamma$ denotes the gamma function and $n!$ denotes the factorial.
Proof
References
- 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): 6.1.2
