Difference between revisions of "Pochhammer symbol with non-negative integer subscript"
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(Created page with "==Theorem== The following formula holds: $$(a)_n = \left\{ \begin{array}{ll} 1, & \quad n=0 \\ a(a+1)\ldots(a+n-1), & \quad n=1,2,3,\ldots. \end{array} \right.$$ ==Proof== =...") |
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$$(a)_n = \left\{ \begin{array}{ll} | $$(a)_n = \left\{ \begin{array}{ll} | ||
1, & \quad n=0 \\ | 1, & \quad n=0 \\ | ||
| − | a(a+1)\ldots(a+n-1), & \quad n=1,2,3,\ldots | + | a(a+1)\ldots(a+n-1), & \quad n=1,2,3,\ldots, |
\end{array} \right.$$ | \end{array} \right.$$ | ||
| + | where $(a)_n$ denotes the [[Pochhammer]] symbol. | ||
==Proof== | ==Proof== | ||
==References== | ==References== | ||
| + | * {{BookReference|Higher Transcendental Functions Volume I|1953|Arthur Erdélyi|author2=Wilhelm Magnus|author3=Fritz Oberhettinger|author4=Francesco G. Tricomi|prev=Pochhammer|next=findme}}: $4.1 (2)$ | ||
[[Category:Theorem]] | [[Category:Theorem]] | ||
[[Category:Unproven]] | [[Category:Unproven]] | ||
Latest revision as of 23:25, 3 March 2018
Theorem
The following formula holds: $$(a)_n = \left\{ \begin{array}{ll} 1, & \quad n=0 \\ a(a+1)\ldots(a+n-1), & \quad n=1,2,3,\ldots, \end{array} \right.$$ where $(a)_n$ denotes the Pochhammer symbol.
Proof
References
- 1953: Arthur Erdélyi, Wilhelm Magnus, Fritz Oberhettinger and Francesco G. Tricomi: Higher Transcendental Functions Volume I ... (previous) ... (next): $4.1 (2)$
