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http://functions.wolfram.com/06.10.09.0001.01
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Pochhammer[a, n] == Limit[m^n Product[(a + k)/(a + n + k), {k, 0, m - 1}],
m -> Infinity]
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Cell[BoxData[RowBox[List[RowBox[List["Pochhammer", "[", RowBox[List["a", ",", "n"]], "]"]], "\[Equal]", RowBox[List["Limit", "[", RowBox[List[RowBox[List[SuperscriptBox["m", "n"], " ", RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["k", "=", "0"]], RowBox[List["m", "-", "1"]]], FractionBox[RowBox[List["a", "+", "k"]], RowBox[List["a", "+", "n", "+", "k"]]]]]]], ",", RowBox[List["m", "\[Rule]", "\[Infinity]"]]]], "]"]]]]]]
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<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <semantics> <msub> <mrow> <mo> ( </mo> <mi> a </mi> <mo> ) </mo> </mrow> <mi> n </mi> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[RowBox[List["(", "a", ")"]], "n"], Pochhammer] </annotation> </semantics> <mo> ⩵ </mo> <mrow> <munder> <mi> lim </mi> <mrow> <mi> m </mi> <semantics> <mo> → </mo> <annotation encoding='Mathematica'> "\[Rule]" </annotation> </semantics> <mi> ∞ </mi> </mrow> </munder> <mo> ⁢ </mo> <mtext>   </mtext> <mrow> <msup> <mi> m </mi> <mi> n </mi> </msup> <mo> ⁢ </mo> <mrow> <munderover> <mo> ∏ </mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mrow> <mi> m </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </munderover> <mfrac> <mrow> <mi> a </mi> <mo> + </mo> <mi> k </mi> </mrow> <mrow> <mi> a </mi> <mo> + </mo> <mi> k </mi> <mo> + </mo> <mi> n </mi> </mrow> </mfrac> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> Pochhammer </ci> <ci> a </ci> <ci> n </ci> </apply> <apply> <limit /> <bvar> <ci> m </ci> </bvar> <condition> <apply> <tendsto /> <ci> m </ci> <infinity /> </apply> </condition> <apply> <times /> <apply> <power /> <ci> m </ci> <ci> n </ci> </apply> <apply> <product /> <bvar> <ci> k </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <apply> <plus /> <ci> m </ci> <cn type='integer'> -1 </cn> </apply> </uplimit> <apply> <times /> <apply> <plus /> <ci> a </ci> <ci> k </ci> </apply> <apply> <power /> <apply> <plus /> <ci> a </ci> <ci> k </ci> <ci> n </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Pochhammer", "[", RowBox[List["a_", ",", "n_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["Limit", "[", RowBox[List[RowBox[List[SuperscriptBox["m", "n"], " ", RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["k", "=", "0"]], RowBox[List["m", "-", "1"]]], FractionBox[RowBox[List["a", "+", "k"]], RowBox[List["a", "+", "n", "+", "k"]]]]]]], ",", RowBox[List["m", "\[Rule]", "\[Infinity]"]]]], "]"]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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